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A complex analysis approach to Atangana-Baleanu fractional calculusMay 16 2019The standard definition for the Atangana-Baleanu fractional derivative involves an integral transform with a Mittag-Leffler function in the kernel. We show that this integral can be rewritten as a complex contour integral which can be used to provide ... More

A Beurling Theorem for almost-invariant subspaces of the shift operatorMay 16 2019A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorem. As a corollary we describe the almost-invariant subspaces for ... More

Holomorphic approximation and mixed boundary value problems for $\partial$May 16 2019In this paper, we study holomorphic approximation using boundary value problems for $\partial$ on an annulus in the Hilbert space setting. The associated boundary conditions for $\partial$ are the mixed boundary problems on an annulus. We characterize ... More

Holomorphic approximation via Dolbeault cohomologyMay 16 2019The purpose of this paper is to study holomorphic approximation and approximation of $\partial$-closed forms in complex manifolds of complex dimension n $\ge$ 1. We consider extensions of the classical Runge theorem and the Mergelyan property to domains ... More

On the extension of holomorphic sections from reduced unions of strata of divisorsMay 16 2019In this paper we study the problem of extension of holomorphic sections of line bundles/vector bundles from reduced unions of strata of divisors. An extension theorem of Ohsawa--Takegoshi type is proved. As consequences we deduce several qualitative results ... More

Infinitesimal symmetries of weakly pseudoconvex manifoldsMay 15 2019We classify the Lie algebras of infinitesimal CR automorphisms of weakly pseudoconvex hypersurfaces of finite multitype in $\mathbb C^N$. In particular, we prove that such manifolds admit neither nonlinear rigid automorphisms, nor real or nilpotent rotations. ... More

On the local and boundary behavior of mappings on factor-spacesMay 15 2019In this article, we study mappings acting between domains of two factor spaces by certain groups of M\"{o}bius automorphisms of the unit ball that act discontinuously and do not have fixed points. For such mappings, we have established estimates for the ... More

Transcendental holomorphic maps between real algebraic manifolds in a complex spaceMay 15 2019We give an example of a real algebraic manifold embedded in a complex space that does not satisfy the Nash-Artin approximation Property. This Nash-Artin approximation Property is closely related to the problem of determining when the biholomorphic equivalence ... More

Higgs bundles and flat connections over compact Sasakian manifoldsMay 15 2019Given a compact K\"ahler manifold $X$, there is an equivalence of categories between the completely reducible flat vector bundles on $X$ and the polystable Higgs bundles $(E,\, \theta)$ on $X$ with $c_1(E)= 0= c_2(E)$ \cite{SimC}, \cite{Cor}, \cite{UY}, ... More

Few results in connection with sum and product theorems of relative $(p,q)$-$\varphi$ order, relative $(p,q)$-$\varphi$ type and relative $(p,q)$-$\varphi$ weak type of meromorphic functions with respect to entire functionsMay 15 2019Orders and types of entire and meromorphic functions have been actively investigated by many authors. In the present paper, we aim at investigating some basic properties in connection with sum and product of relative $(p,q)$-$\varphi$ order, relative ... More

Mabuchi's soliton metric and relative D-stabilityMay 15 2019For Fano manifolds T. Mabuchi introduced a generalization of the K\"ahler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a Fano manifold admits Mabuchi's metric if and only if it is uniformly ... More

An example of a symmetric homeomorphism of the real line with non-symmetric inversionMay 15 2019We show an example of a symmetric homeomorphism $h$ of the real line $\mathbb{R}$ onto itself such that $h^{-1}$ is not symmetric. This implies that the set of all symmetric self-homeomorphisms of $\mathbb{R}$ does not constitute a group under the composition. ... More

Game Theoretic Optimization via Gradient-based Nikaido-Isoda FunctionMay 15 2019Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda ... More

A Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factorMay 14 2019We provide a short argument to establish a Beurling-Lax-Halmos theorem for reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick factor. We also record factorization results for pairs of nested invariant subspaces.

A complete normal form for everywhere Levi degenerate hypersurfaces in $\mathbb C^{3}$May 14 2019In this paper, we construct a complete convergent normal form for everywhere $2$-nondegenerate real-analytic hypersurfaces in complex $3$-space. We do so by developing Moser's homological approach in the $2$-nondegenerate setting. This seems to be the ... More

Coefficient and Radius Estimates Of Starlike Functions with positive real partMay 14 2019Let $\mathscr{S}^*_e$ and $\mathscr{S}^*_\mathcal{R}$ denote the classes of analytic functions $f$ in the open unit disk normalized by conditions $f(0)=0$ and $f'(0)=1$ satisfying the subordination $zf'(z)/f(z)\prec e^z$ and $zf'(z)/f(z)\prec 1+z(k+z)/(k(k-z))=:\varphi_\mathcal{R}(z)$ ... More

Convolutional neural networks with fractional order gradient methodMay 14 2019This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified fractional order gradient ... More

On tangency in equisingular families of curves and surfacesMay 13 2019We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the $s$-invariant of a curve and we show that in a Whitney equisingular family with the property that ... More

Monomial convergence on $\ell_r$May 13 2019For $1 < r \le 2$, we study the set of monomial convergence for spaces of holomorphic functions over $\ell_r$. For $ H_b(\ell_r)$, the space of entire functions of bounded type in $\ell_r$, we prove that $\mbox{mon} H_b(\ell_r)$ is exactly the Marcinkiewicz ... More

ProfessorMay 13 2019We give a proof of the well-known fact that the $\Ok$-module $\E$ of smooth functions is flat by means of residue theory and integral formulas. A variant of the proof gives a related statement for classes of functions of lower regularity. We also prove ... More

The flatness of the $\Ok$-module of smooth functions and integral representationMay 13 2019May 14 2019We give a proof of the well-known fact that the $\Ok$-module $\E$ of smooth functions is flat by means of residue theory and integral formulas. A variant of the proof gives a related statement for classes of functions of lower regularity. We also prove ... More

Oscillation of Functions in the Hölder classMay 13 2019We study the size of the set of points where the $\alpha$-divided difference of a function in the H\"older class $\Lambda_\alpha$ is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated ... More

The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer ordersMay 10 2019Let $\Omega\subset\mathbb{C}^m$ be a bounded pseudoconvex domain with smooth boundary. For each $k\in\mathbb{N}$, we give a sufficient condition to estimate the $\bar\partial$-Neumann operator in the Sobolev space $W^k(\Omega)$. The key feature of our ... More

On subvarieties of singular quotients of bounded domainsMay 10 2019Let $X$ be a quotient of a bounded domain in $\mathbb C^n$. Under suitable assumptions, we prove that every subvariety of $X$ not included in the branch locus of the quotient map is of log general type in some orbifold sense, generalizing Boucksom and ... More

Phase retrieval for wide-band signalsMay 10 2019This study investigates the phase retrieval problem for wide-band signals. We solve the following problem: given f $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x|} dx), we find all functions g $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x| ... More

Critical points of random branched coverings of the Riemann sphereMay 10 2019Given a closed Riemann surface $\Sigma$ equipped with a volume form $\omega$, we construct a natural probability measure on the space $\mathcal{M}_d(\Sigma)$ of degree $d$ branched coverings from $\Sigma$ to the Riemann sphere $\mathbb{C}\mathbb{P}^1.$ ... More

Splitting hairs with transcendental entire functionsMay 09 2019Many authors have studied the dynamics of functions in the \emph{Eremenko-Lyubich class} $\mathcal{B}$; this class consists of those transcendental entire functions for which the set of singular values is bounded. With the additional assumption that the ... More

Learning Representations for Predicting Future ActivitiesMay 09 2019Foreseeing the future is one of the key factors of intelligence. It involves understanding of the past and current environment as well as decent experience of its possible dynamics. In this work, we address future prediction at the abstract level of activities. ... More

A Novel Adaptive Kernel for the RBF Neural NetworksMay 09 2019In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework ... More

CR eigenvalue estimate and Kohn-Rossi cohomologyMay 09 2019May 11 2019Let $X$ be a compact connected CR manifold with a transversal CR $S^1$-action of dimension $2n-1$, which is only assumed to be weakly pseudoconvex. Let $\Box_b$ be the $\overline{\partial}_b$-Laplacian. Eigenvalue estimate of $\Box_b$ is a fundamental ... More

CR eigenvalue estimate and Kohn-Rossi cohomologyMay 09 2019Let $X$ be a compact connected weakly pseudo-convex CR manifold with a transversal CR $S^1$-action of dimension $2n-1$. Generalizing Berndtsson's eigenvalue estimate for the $\bar \partial$ Laplacian to CR setting, we obtain a sharp estimate of the number ... More

Asymptotic estimate of cohomology groups valued in pseudo-effective line bundlesMay 09 2019In this paper, we study questions of Demailly and Matsumura on the asymptotic behavior of dimensions of cohomology groups for high tensor powers of (nef) pseudo-effective line bundles over non-necessarily projective algebraic manifolds. By generalizing ... More

MAP Inference via L2-Sphere Linear Program ReformulationMay 09 2019Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation methods have been ... More

Renormalization in the Golden-Mean Semi-Siegel Hénon Family: Non-QuasisymmetryMay 08 2019For quadratic polynomials of one complex variable, the boundary of the golden-mean Siegel disk must be a quasicircle. We show that the analogous statement is not true for quadratic H\'enon maps of two complex variables.

Value range of solutions to the chordal Loewner equation with restriction on the driving functionMay 08 2019We consider a value range $\{g(i,T)\}$ of solutions to the chordal Loewner equation with the restriction $|\lambda(t)| \le c$ on the driving function. We use reachable set methods and the Pontryagin maximum principle.

Value range of solutions to the chordal Loewner equation with restriction on the driving functionMay 08 2019May 14 2019We consider a value range $\{g(i,T)\}$ of solutions to the chordal Loewner equation with the restriction $|\lambda(t)| \le c$ on the driving function. We use reachable set methods and the Pontryagin maximum principle.

A summation method based on the Fourier series of periodic distributions and an exampleMay 08 2019A generalised summation method is considered based on the Fourier series of periodic distributions. It is shown that $$ e^{it}-2e^{2it}+3e^{3it}-4e^{4it}+-\cdots = {\mathrm P\mathrm f} {\displaystyle \frac{e^{it}}{(1+e^{it})^2}} +i\pi \displaystyle \sum_{n\in ... More

Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metricsMay 08 2019We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal K\"{a}hler manifold with constant nonpositive holomorphic sectional curvature is K\"{a}hler. We ... More

Volume of Perturbations of Pseudoeffective ClassesMay 08 2019In this short note, we consider the question of determining the asymptotics of the volume function near the boundary of the pseudoeffective cone on compact K\"ahler manifolds. We solve the question in a number of cases -- in particular, we show that the ... More

Factorization of symplectic matrices into elementary factorsMay 07 2019We prove that a symplectic matrix with entries in a ring with Bass stable rank one can be factored as a product of elementary symplectic matrices. This also holds for null-homotopic symplectic matrices with entries in a Banach algebra or in the ring of ... More

On metrics of constant positive curvature with four conic singularities on the sphereMay 07 2019We show that for given four points on the sphere and prescribed angles at these points, which are not multiples of $2\pi$, the number of metrics of curvature 1 having conic singularities with these angles at these points is finite.

An algebra of polyanalytic functionsMay 07 2019The most important uniform algebra is the family of continuous functions on a compact subset $K$ of the complex plane $\mathbb{C}$ which are analytic on the interior int$(K)$ For compact sets $K$ which are regular (i.e. $K =$int$(K)$ and for polyanalytic ... More

Computation of Circular Area and Spherical Volume Invariants via Boundary IntegralsMay 06 2019We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume integrals as line and ... More

On a class of Kato manifoldsMay 06 2019We revisit Brunella's proof of the fact that Kato surfaces admit locally conformally K\"ahler metrics, and we show that it holds for any complex manifold containing a global spherical shell. We consider a specific class of these manifolds, which can be ... More

A note on Flenner's extension theoremMay 06 2019We show that any $p$-form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as long as $p \le \mathrm{codim}_X (X_{\mathrm{sg}}) - 2$, where $c$ is the codimension of the singular ... More

On Heinz type inequality and Lipschitz characteristic for mappings satisfying polyharmonic equationsMay 06 2019For $K\geq1$, suppose that $f$ is a $K$-quasiconformal self-mapping of the unit ball $\mathbb{B}^{n}$, which satisfies the following: $(1)$ the polyharmonic equation $\Delta^{m}f=\Delta(\Delta^{m-1} f)$$=\varphi_{m}$ $(\varphi_{m}\in\mathcal{C}(\overline{\mathbb{B}^{n}},\mathbb{R}^{n}))$, ... More

On asymptotically sharp bi-Lipschitz inequalities of quasiconformal mappings satisfying inhomogeneous polyharmonic equationsMay 06 2019Suppose that $f$ is a $K$-quasiconformal ($(K,K')$-quasiconformal resp.) self-mapping of the unit disk $\mathbb{D}$, which satisfies the following: $(1)$ the inhomogeneous polyharmonic equation $\Delta^{n}f=\Delta(\Delta^{n-1} f)=\varphi_{n}$ $(\varphi_{n}\in ... More

Modulus of continuity and Heinz-Schwarz type inequalities of solutions to inhomogeneous biharmonic Dirichlet problemsMay 06 2019For positive integers $n\geq2$ and $m\geq1$, suppose that function $f\in\mathcal{C}^{4}(\mathbb{B}^{n},\mathbb{R}^{m})\cap\mathcal{C}^{1}(\overline{\mathbb{B}^{n}},\mathbb{R}^{m})$ satisfying the following: $(1)$ the inhomogeneous biharmonic equation ... More

Global existence and convergence for the CR Q-curvature flow in a closed strictly pseudoconvex CR 3-manifoldMay 06 2019In this note, we affirm the partial answer to the long open Conjecture which states that any closed strictly pseudoconvex CR $3$-manifold admits a contact form $\theta $ with the vanishing CR $Q$-curvature. More precisely, we deform the contact form according ... More

Differential Inequalities and Univalent FunctionsMay 05 2019Let ${\mathcal M}$ be the class of analytic functions in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition $$\left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right |\leq 1, \quad ... More

On classes of meromorphic locally univalent functions defined by differential inequalitiesMay 05 2019n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for further research. ... More

Exponential factorizations of holomorphic mapsMay 05 2019We show that any element of the special linear group $SL_2(R)$ is a product of two exponentials if the ring $R$ is either the ring of holomorphic functions on an open Riemann surface or the disc algebra. This is sharp: one exponential factor is not enough ... More

Relations among spheroidal and spherical harmonicsMay 04 2019A contragenic function in a domain $\Omega\subseteq\mathbf{R}^3$ is a reduced-quaternion-valued (i.e. the last coordinate function is zero) harmonic function, which is orthogonal in $L^2(\Omega)$ to all monogenic functions and their conjugates. The notion ... More

Projective Freeness of Algebras of Bounded Holomorphic Functions on Infinitely Connected DomainsMay 04 2019The algebra $H^\infty(D)$ of bounded holomorphic functions on $D\subset\mathbb C$ is projective free for a wide class of infinitely connected domains. In particular, for such $D$ every rectangular left-invertible matrix with entries in $H^\infty(D)$ can ... More

Convergence of the weak Kähler-Ricci Flow on manifolds of general typeMay 03 2019We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique ... More

Analytic continuation for solutions to the system of trinomial algebraic equationsMay 03 2019In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system. In particular, we develop the idea of applying the Mellin-Barnes integral representation ... More

Non-autonomous Parabolic BifurcationMay 02 2019Let $f(z) = z+z^2+O(z^3)$ and $f_\epsilon(z) = f(z) + \epsilon^2$. A classical result in parabolic bifurcation in one complex variable is the following: if $N-\frac{\pi}{\epsilon}\to 0$ we obtain $(f_\epsilon)^{N} \to \mathcal{L}_f$, where $\mathcal{L}_f$ ... More

Of commutators and JacobiansMay 02 2019I discuss the prescribed Jacobian equation $Ju=\det\nabla u=f$ for an unknown vector-function $u$, and the connection of this problem to the boundedness of commutators of multiplication operators with singular integrals in general, and with the Beurling ... More

Conformal covariance of the Liouville quantum gravity metric for $γ \in (0,2)$May 01 2019For $\gamma \in (0,2)$, $U\subset \mathbb C$, and an instance $h$ of the Gaussian free field (GFF) on $U$, the $\gamma$-Liouville quantum gravity (LQG) surface associated with $(U,h)$ is formally described by the Riemannian metric tensor $e^{\gamma h} ... More

Existence and uniqueness of the Liouville quantum gravity metric for $γ\in (0,2)$May 01 2019We show that for each $\gamma \in (0,2)$, there is a unique metric associated with $\gamma$-Liouville quantum gravity (LQG). More precisely, we show that for the whole-plane Gaussian free field (GFF) $h$, there is a unique random metric $D_h = "e^{\gamma ... More

Confluence of geodesics in Liouville quantum gravity for $γ\in (0,2)$May 01 2019We prove that for any metric which one can associate with a Liouville quantum gravity (LQG) surface for $\gamma \in (0,2)$ satisfying certain natural axioms, its geodesics exhibit the following confluence property. For any fixed point $z$, a.s. any two ... More

On the existence of Kobayashi and Bergman metrics for Model domainsApr 29 2019May 02 2019We prove that for a pseudoconvex domain of the form $\mathfrak{A} = \{(z, w) \in \mathbb C^2 : v > F(z, u)\}$, where $w = u + iv$ and F is a continuous function on ${\mathbb C}_z \times {\mathbb R}_u$, the following conditions are equivalent: (1) The ... More

On the existence of Kobayashi and Bergman metrics for Model domainsApr 29 2019We prove that for a pseudoconvex domain of the form $\mathfrak{A} = \{(z, w) \in \mathbb C^2 : v > F(z, u)\}$, where $w = u + iv$ and F is a continuous function on ${\mathbb C}_z \times {\mathbb R}_u$, the following conditions are equivalent: \begin{enumerate} ... More

On the existence of Kobayashi and Bergman metrics for Model domainsApr 29 2019May 06 2019We prove that for a pseudoconvex domain of the form $\mathfrak{A} = \{(z, w) \in \mathbb C^2 : v > F(z, u)\}$, where $w = u + iv$ and F is a continuous function on ${\mathbb C}_z \times {\mathbb R}_u$, the following conditions are equivalent: (1) The ... More

On proper branched coverings and a question of VuorinenApr 29 2019We study global injectivity of proper branched coverings defined on the Euclidean $n$-ball in the case when the branch set is compact. In particular we show that such mappings are homeomorphisms when $n=3$ or when the branch set is empty. This proves ... More

Random interpolating sequences in Dirichlet spacesApr 29 2019We discuss random interpolating sequences in weighted Dirichlet spaces $\mathcal{D}_\alpha$, $0\leq \alpha\leq 1$. Our results in particular imply that almost sure interpolating sequences for $\mathcal{D}_\alpha$ are exactly the almost sure separated ... More

On Hyperbolic Polynomials and Four-term Recurrence with Linear CoefficientsApr 29 2019For any real numbers $a,\ b$, and $c$, we form the sequence of polynomials $\{P_n(z)\}_{n=0}^\infty$ satisfying the four-term recurrence \[ P_n(z)+azP_{n-1}(z)+bP_{n-2}(z)+czP_{n-3}(z)=0,\ n\in\mathbb{N}, \] with the initial conditions $P_0(z)=1$ and ... More

On the Wong-Rosay theoremApr 28 2019We prove a Wong-Rosay type theorem for a domain with a piecewise smooth generic strictly pseudoconvex boundary point.

Some remarks on the Cegrell's class $\mathcal{F}$Apr 28 2019In this paper, we study the near-boundary behavior of functions $u\in\mathcal{F}(\Omega)$ in the case where $\Omega$ is strictly pseudoconvex. We also introduce a sufficient condition for belonging to $\mathcal{F}$ in the case where $\Omega$ is the unit ... More

On the Poincaré problem for foliations on compact toric orbifoldsApr 27 2019We give an optimal upper bound of the degree of quasi-smooth hypersurfaces which are invariant by a one-dimensional holomorphic foliation on a compact toric orbifold, i.e. on a complete simplicial toric variety. This bound depends only on the degree of ... More

Collage Inference: Tolerating Stragglers in Distributed Neural Network Inference using CodingApr 27 2019MLaaS (ML-as-a-Service) offerings by cloud computing platforms are becoming increasingly popular these days. Pre-trained machine learning models are deployed on the cloud to support prediction based applications and services. For achieving higher throughput, ... More

Arestov's theorems on Bernstein's inequalityApr 26 2019We give a simple, elementary, and at least partially new proof of Arestov's famous extension of Bernstein's inequality in $L_p$ to all $p \geq 0$. Our crucial observation is that Boyd's approach to prove Mahler's inequality for algebraic polynomials $P_n ... More

Dynamics of generalised exponential mapsApr 26 2019Since 1984, many authors have studied the dynamics of maps of the form $\mathcal{E}_a(z) = e^z - a$, with $a > 1$. It is now well-known that the Julia set of such a map has an intricate topological structure known as a Cantor bouquet, and much is known ... More

D'Angelo conjecture in the third gap intervalApr 26 2019We show the D'Angelo conjecture holds in the third gap interval. More precisely, we prove that the degree of any rational proper holomorphic map from $\mathbb{B}^n$ to $\mathbb{B}^{4n-6}$ with $n\geq 7$ is not more than $3$.

The algebraic dimension of compact complex threefolds with vanishing second Betti numbersApr 25 2019The paper \cite{CDP98} studied compact complex threefolds $X$ such that the second Betti number $b_2(X) = 0.$ The main result is based on Lemma 1.5, which happens to be incorrect in general (but might still hold in the context of the paper). In any case, ... More

On the Koebe Quarter Theorem for PolynomialsApr 24 2019D. Dimitrov has posed the problem of finding polynomials that set the sharpness of the Koebe Quarter Theorem for polynomials and asked whether Suffridge polynomials are optimal. We disprove Dimitrov's conjecture for polynomials of degree 3, 4, 5 and 6. ... More

Analytical solutions for two-dimensional singly periodic Stokes flow singularity arrays near wallsApr 24 2019New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric ... More

Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric AssignmentApr 24 2019This paper introduces the unsupervised assignment flow that couples the assignment flow for supervised image labeling with Riemannian gradient flows for label evolution on feature manifolds. The latter component of the approach encompasses extensions ... More

Subelliptic estimates from Gromov hyperbolicityApr 24 2019In this paper we prove: if the complete K\"ahler-Einstein metric on a bounded convex domain (with no boundary regularity assumptions) is Gromov hyperbolic, then the $\overline{\partial}$-Neumann problem satisfies a subelliptic estimate. We also provide ... More

On the sum of squares of the coefficients of Bloch functionsApr 24 2019In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

Closed range estimates for $\bar\partial_b$ on CR manifolds of hypersurface typeApr 24 2019The purpose of this paper is to establish sufficient conditions for closed range estimates on $(0,q)$-forms, for some fixed $q$, $1 \leq q \leq n-1$, for $\bar\partial_b$ in both $L^2$ and $L^2$-Sobolev spaces in embedded, not necessarily pseudoconvex ... More

A note on Fox's H function in the light of Braaksma's resultsApr 24 2019In our previous works we found a power series expansion of a particular case of Fox's $H$ function $H^{q,0}_{p,q}$ in a neighborhood of its positive singularity. An inverse factorial series expansion of the integrand of $H^{q,0}_{p,q}$ served as our main ... More

Sets of uniqueness, weakly sufficient sets and sampling sets for weighted spaces of holomorphic functions in the unit ballApr 24 2019We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $\mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the equivalence ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on Hartogs triangle. The estimates of the operator norm are in terms ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019Apr 25 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on Hartogs triangle. The estimates of the operator norm are in terms ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019May 01 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the operator norm are ... More

Weighted estimates for the $\bar{\partial}$-Neumann problem on intersections of strictly pseudoconvex domains in $\mathbb{C}^2$Apr 23 2019We obtain weighted estimates for the $\bar{\partial}$-Neumann operator on intersections of two smooth strictly pseudoconvex domains in $\mathbb{C}^2$. The regularity estimates are described with the use of Sobolev norms with weights which are powers of ... More

Nonvanishing of Cartan CR curvature on boundaries of Grauert tubes around hyperbolic surfacesApr 23 2019We show that the boundaries of thin strongly pseudoconvex Grauert tubes, with respect to the Guillemin-Stenzel K\"{a}hler metric canonically associated with the Poincar\'e metric on closed hyperbolic real-analytic surfaces, has nowhere vanishing Cartan ... More

Oscillating Wandering Domains for Functions with Escaping Singular ValuesApr 22 2019We construct a transcendental entire $f:\mathbb{C}\rightarrow\mathbb{C}$ such that (1) $f$ has bounded singular set, (2) $f$ has a wandering domain, and (3) each singular value of $f$ escapes to infinity under iteration by $f$.

A Schwarz lemma for two domains in $\mathbb C^n$ and complex geometryApr 22 2019We make sharp estimates to obtain a Schwarz type lemma for the symmetrized polydisc $\mathbb{G}_n$ and for the extended symmetrized polydisc $\tilde{\mathbb{G}}_n$. We explicitly construct an interpolating function under certain condition. Also we find ... More

On bicomplex Fourier--Wigner transformsApr 20 2019We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional spaces are discussed. ... More

Product domains, Multi-Cauchy transforms, and the $\bar \partial$ equationApr 20 2019Solution operators for the equation $\bar \partial u=f$ are constructed on general product domains in $\mathbb{C}^n$. When the factors are one-dimensional, the operator is a simple integral operator: it involves specific derivatives of $f$ integrated ... More

Strong Closed Range Estimates: Necessary Conditions and ApplicationsApr 19 2019The $L^2$ theory of the $\bar\partial$ operator on domains in $\mathbb{C}^n$ is predicated on establishing a good basic estimate. Typically, one proves not a single basic estimate but a family of basic estimates that we call a family of strong closed ... More

General derivative Thomae formula for singular half-periodsApr 19 2019The paper develops the result of second Thomae theorem in hyperelliptic case, that is values at zero of the lowest non-vanishing derivatives of theta functions with singular characteristics of arbitrary multiplicity are expressed in terms of branch points ... More

On maximally totally real embeddingsApr 19 2019We consider complex structures with totally real zero section of the tangent bundle. We assume that the complex structure tensor is real-analytic along the fibers of the tangent bundle. This assumption is quite natural in view of a well known result by ... More

Deformation and quasiregular extension of cubical Alexander mapsApr 19 2019In this article we prove that, for an oriented PL $n$-manifold $M$ with $m$ boundary components and $d_0\in \mathbb N$, there exist mutually disjoint closed Euclidean balls and a $\mathsf K$-quasiregular mapping $M \to \mathbb S^n \setminus \mathrm{int}(B_1\cup ... More

Co-isometric weighted composition operators on Hilbert spaces of analytic functionsApr 18 2019We consider a very general family of Hilbert spaces of analytic functions in the unit disk which satisfy only a minimum number of requirements and whose reproducing kernels have the usual natural form. Under such assumptions, we obtain a necessary and ... More

Co-isometric weighted composition operators on Hilbert spaces of analytic functionsApr 18 2019May 01 2019We consider a very general family of Hilbert spaces of analytic functions in the unit disk which satisfy only a minimum number of requirements and whose reproducing kernels have the usual natural form. Under such assumptions, we obtain a necessary and ... More

Some Aspect of Certain two Subclass of Analytic Functions with Negative Coefficients Defined by Rafid OperatorApr 18 2019In this paper, we define the subclasses $R_{\mu,p}^{\delta}(\alpha;A,B)\ $ and $ P_{\mu,p}^{\delta}(\alpha;A,B)\ $ of analytic functions in the open unit disc of complex plain. Then the neighborhood properties, integral means inequalities and some results ... More

On The Classification-Distortion-Perception TradeoffApr 18 2019Signal degradation is ubiquitous and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the perception-distortion tradeoff, ... More