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Quasiregular curvesSep 18 2019We extend the notion of a pseudoholomorphic vector of Iwaniec, Verchota, and Vogel to mappings between Riemannian manifolds. Since this class of mappings contains both quasiregular mappings and (pseudo)holomorphic curves, we call them quasiregular curves. ... More

Sums of random polynomials with independent rootsSep 17 2019We consider the zeros of the sum of independent random polynomials as their degrees tend to infinity. Namely, let $p$ and $q$ be two independent random polynomials of degree $n$, whose roots are chosen independently from the probability measures $\mu$ ... More

Angular Derivatives and Boundary Values of H(b) Spaces of Unit Ball of $\mathbb{C}^n$Sep 17 2019In this work we study deBranges-Rovnyak spaces, $H(b)$, on the unit ball of $\mathbb{C}^n$. We give an integral representation of the functions in $H(b)$ through the Clark measure on $S^n$ associated with $b$. A characterization of admissible boundary ... More

A Convergence Proof of Projected Fast Iterative Soft-thresholding Algorithm for Parallel Magnetic Resonance ImagingSep 17 2019The boom of non-uniform sampling and compressed sensing techniques dramatically alleviates the prolonged data acquisition problem of magnetic resonance imaging. Sparse reconstruction, thanks to its fast computation and promising performance, has attracted ... More

Uniform asymptotics of Toeplitz determinants with Fisher-Hartwig singularitiesSep 16 2019We obtain an asymptotic formula for $n\times n$ Toeplitz determinants as $n\to \infty$, for real valued symbols with any fixed number of Fisher-Hartwig singularities, which is uniform with respect to the location of the singularities. As an application, ... More

Quadratic differentials and circle patterns on complex projective toriSep 16 2019Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cross ratio system induces a complex projective structure together with a ... More

Pluripotential solutions versus viscosity solutions to complex Monge-Amp{è}re flowsSep 16 2019We compare various notions of weak subsolutions to degenerate complex Monge-Amp{\`e}re flows, showing that they all coincide. This allows us to show that the viscosity solution coincides with the envelope of pluripotential subsolutions. Dedicated to Duong ... More

Hermitian metrics on the anti-canonical bundle of the blow-up of the projective plane at nine pointsSep 15 2019We investigate Hermitian metrics on the anti-canonical bundle of a rational surface obtained by blowing up the projective plane at nine points. For that purpose, we pose a modified variant of an argument made by Ueda on the complex analytic structure ... More

Classification of foliations by curves of low degree on the three-dimensional projective spaceSep 14 2019We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of such foliations by curves up to degree 3, also ... More

Characteristic polynomials of complex random matrices and Painlevé transcendentsSep 13 2019We study expectations of powers and correlation functions for characteristic polynomials of $N \times N$ non-Hermitian random matrices. For the $1$-point and $2$-point correlation function, we obtain several characterizations in terms of Painlev\'e transcendents, ... More

Non-uniform Hyperbolicity In Polynomial Skew ProductsSep 13 2019Let $f:\mathbb{C}^2\to \mathbb{C}^2$ be a polynomial skew product which leaves invariant an attracting vertical line $ L $. Assume moreover $f$ restricted to $L$ is non-uniformly hyperbolic, in the sense that $f$ restricted to $L$ satisfies one of the ... More

Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangleSep 12 2019In this paper, we investigate the weak-type regularity of the Bergman projection. The two domains we focus on are the polydisc and the Hartogs triangle. For the polydisc we provide a proof that the weak-type behavior is of "$L\log L$" type. This result ... More

A new approach for the univalence of certain integral of harmonic mappingsSep 12 2019The principal goal of this paper is to extend the classical problem of find the values of $\alpha\in \C$ for which the mappings, either $F_\alpha(z)=\int_0^z(f(\zeta)/\zeta)^\alpha d\zeta$ or $f_\alpha(z)=\int_0^z(f'(\zeta))^\alpha d\zeta$ are univalent, ... More

Modular forms from the Weierstrass functionsSep 12 2019We construct holomorphic elliptic modular forms of weight 2 and weight 1, by special values of Weierstrass p-functions, and by differences of special values of Weierstrass zeta-functions, respectively. Also we calculated the values of these forms at some ... More

Homomorphisms between algebras of holomorphic functions on the infinite polydiskSep 11 2019We study the vector-valued spectrum $\mathcal{M}_\infty(B_{c_0},B_{c_0})$, that is, the set of non null algebra homomorphisms from $\mathcal H^\infty(B_{c_0})$ to $\mathcal H^\infty(B_{c_0})$ which is naturally projected onto the closed unit ball of $\mathcal ... More

Sharp pointwice estimate for fock spacesSep 11 2019Firstly we establish a sharp pointwise estimate for the arbitrary derivative of the function $f\in F_{\alpha}^{p},$ where $F_{\alpha}^{p}$ denotes the Fock space for $1\leq p<\infty.$ Then, in a particular Hilbert case when $p=2$ we establish another ... More

Some geometric properties of the solutions of complex multi-affine polynomials of degree threeSep 11 2019In this paper, we consider complex polynomials of degree three with distinct zeros and their polarization ((z1,z2,z3) with three complex variables. We show, through elementary means, that the variety P(z1,z2,z3)=0 is birationally equivalent to the variety ... More

A CR singular analogue of Severi's theoremSep 10 2019Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that completely characterizes those quadric CR singular manifolds ... More

Sufficient Conditions and Radius Problems for a starlike Class Involving a Differential InequalitySep 10 2019Let $\mathcal{A}_n$ be the class of analytic functions $f(z)$ of the form $f(z)=z+\sum_{k=n+1}^\infty a_kz^k,n\in\mathbb{N}$ and let \begin{align*} \Omega_n:=\left\{f\in\mathcal{A}_n:\left|zf'(z)-f(z)\right|<\frac{1}{2},\; z\in\mathbb{D}\right\}. \end{align*} ... More

Some observations concerning polynomial convexitySep 09 2019In this paper we discuss a couple of observations related to polynomial convexity. More precisely, (i) We observe that the union of finitely many disjoint closed balls with centres in $\cup_{\theta\in[0,\pi/2]}e^{i\theta}V$ is polynomially convex, where ... More

Certain smooth real surfaces in $\mathbb{C}^2$ with singularitySep 09 2019Under certain geometric condition, the surfaces in $\mathbb{C}^2$ with isolated CR singularity at the origin and with cubic lowest degree homogeneous term in its graph near the origin, can be reduced, up to biholomorphism of $\mathbb{C}^2$, to a one parameter ... More

Sup-norm Estimates for $\overline{\partial}$ in $\mathbb{C}^3$Sep 09 2019We prove sup-norm estimates for $\overline{\partial}$ on wide class of pseudoconvex domains in $\mathbb{C}^3$, including all known examples of bounded, pseudoconvex domains with real-analytic boundary of finite D'Angelo type.

Dolbeault cohomology of compact complex manifolds with an action of a complex Lie groupSep 09 2019Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute ... More

$L^{1}$ metric geometry of potentials with prescribed singularities on compact Kähler manifoldsSep 09 2019Given $(X,\omega)$ compact K\"ahler manifold and $\psi\in\mathcal{M}^{+}\subset PSH(X,\omega)$ a model type envelope with non-zero mass, i.e. a fixed potential determing some singularities such that $\int_{X}(\omega+dd^{c}\psi)^{n}>0$, we prove that the ... More

The sigma function over a family of cyclic trigonal curves with a singular fiberSep 09 2019In this paper we investigate the behavior of the sigma function over the family of cyclic trigonal curves $X_s$ defined by the equation $y^3 =x(x-s)(x-b_1)(x-b_2)$ in the affine $(x,y)$ plane, for $s\in D_\varepsilon:=\{s \in \mathbb{C} | |s|<\varepsilon\}$. ... More

Bergman kernel on Riemann surfaces and Kaehler metric on symmetric productsSep 09 2019Let $X$ be a compact hyperbolic Riemann surface equipped with the Poincar\'e metric. For any integer $k\geq 2$, we investigate the Bergman kernel associated to the holomorphic Hermitian line bundle $\Omega^{\otimes k}_X$, where $\O$ is the holomorphic ... More

Embedding Theorem For Weighted Hardy Spaces into Lebesgue SpacesSep 09 2019In this paper, we consider the weighted Hardy space $\mathcal{H}^p(\omega)$ induced by an $A_1$ weight $\omega.$ We characterize the positive Borel measure $\mu$ such that the identical operator maps $\mathcal{H}^p(\omega)$ into $L^q(d\mu)$ boundedly ... More

Deformations of Dolbeault cohomology classesSep 09 2019In this paper, we establish a deformation theory for Dolbeault cohomology classes valued in holomorphic tensor bundles. We prove the extension equation which will paly the role of Maurer-Cartan equation. Following the classical theory of Kodaira-Spencer-Kuranishi, ... More

Universal Taylor Series on products of planar domainsSep 08 2019Using a recent Mergelyan type theorem for products of planar compact sets we establish generic existence of Universal Taylor Series on products of planar simply connected domains Omegai, i=1, . . . , d. The universal approximation is realized by partial ... More

Extreme points and support points of families of harmonic Bloch mappingsSep 08 2019In this paper, the main aim is to discuss the existence of the extreme points and support points of families of harmonic Bloch mappings and little harmonic Bloch mappings. First, in terms of the Bloch unit-valued set, we prove a necessary condition for ... More

Inverse Problems for Jacobi Operators with Mixed Spectral DataSep 08 2019We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We also solve this ... More

Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidiskSep 07 2019This paper is a continuation of work done in \cite{BS}. It contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpolating sequences and a Toeplitz corona theorem.

Bergman Kernels of Elementary Reinhardt DomainsSep 07 2019We study the Bergman kernel of certain domains in $\mathbb{C}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational function of ... More

Schwarz type lemmas for pseudo-Hermitian manifoldsSep 06 2019In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the \emph{CR} maps and the transversally holomorphic maps. In terms of some sub-Laplacian or Hessian type Bochner formulas, and comparison ... More

On Orlicz-Sobolev classes on factor spacesSep 06 2019We study the factor-spaces of the unit ball of dimension, not less than three, by a certain group of M\"{o}bius transformations. For mappings of such spaces, an estimate of the distortion of the modulus of families of spheres is obtained. As applications, ... More

Recovery of Future Data via Convolution Nuclear Norm MinimizationSep 06 2019This paper is about recovering the unseen future data from a given sequence of historical samples, so called as \emph{future data recovery}---a significant problem closely related to time series forecasting. To address the problem, it is now prevalent ... More

A view on elliptic integrals from primitive forms (Period integrals of type $\mathrm{A_2, B_2}$ and $\mathrm{G_2}$Sep 06 2019Elliptic integrals, since Euler's finding of addition theorem 1751, has been studied extensively from various view points. Present paper gives a short summery of a view point from primitive integrals of types $\mathrm{A_2}, \mathrm{B_2}$ and $\mathrm{G_2}$. ... More

Complex Hessian equations with prescribed singularity on compact Kähler manifoldsSep 05 2019Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $1\leq m\leq n$. We prove that the total mass of the complex Hessian measure of $\omega$-$m$-subharmonic functions is non-decreasing with respect to the singularity type. We then ... More

Equivariant functions and rational differential operatorsSep 04 2019We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function algebras in several ... More

Derivatives of Blaschke Products and Model Space FunctionsSep 04 2019The relationship between the distribution of zeros of an infinite Blaschke product $B$ and the inclusion in weighted Bergman spaces $A_{\alpha}^p$ of the derivative of $B$ or the derivative of functions in its model space $H^2 \ominus BH^2$ is investigated. ... More

The ML-EM algorithm in continuum: sparse measure solutionsSep 04 2019Linear inverse problems $A \mu = \delta$ with Poisson noise and non-negative unknown $\mu \geq 0$ are ubiquitous in applications, for instance in Positron Emission Tomography (PET) in medical imaging. The associated maximum likelihood problem is routinely ... More

Clark measures on the torusSep 04 2019Let $\mathbb{D}$ denote the unit disc of $\mathbb{C}$ and let $\mathbb{T}= \partial\mathbb{D}$. Given a holomorphic function $\varphi: \mathbb{D}^n \to \mathbb{D}$, $n\ge 2$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\mathbb{T}$, ... More

Optimal translational-rotational invariant dictionaries for imagesSep 04 2019We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques. Optimality is considered ... More

Meromorphic mappings of a complete connected Kähler manifold into a projective space sharing hyperplanesSep 04 2019Let $M$ be a complete K\"{a}hler manifold, whose universal covering is biholomorphic to a ball in $\mathbb C^m$. In this article, we will show that if three meromorphic mappings $f^1,f^2,f^3$ of $M$ into $\mathbb P^n(\mathbb C)\ (n\ge 2)$ satisfying the ... More

Reachable states and holomorphic function spaces for the 1-D heat equationSep 04 2019The description of the reachable states of the heat equation is one of the central questions in control theory. The aim of this work is to present new results for the 1-D heat equation with boundary control on the segment $[0, \pi]$. In this situation ... More

Une nouvelle démonstration de la classification des feuilletages convexes de degré deux sur $\mathbb P^2_{\mathbb C}$Sep 04 2019A holomorphic foliation on $\mathbb P^2_{\mathbb C}$, or a real analytic foliation on $\mathbb{P}^{2}_{\mathbb{R}},$ is said to be convex if its leaves other than straight lines have no inflection points. The classification of the convex foliations of ... More

Functional Asplund's metrics for pattern matching robust to variable lighting conditionsSep 04 2019In this paper, we propose a complete framework to process images captured under uncontrolled lighting and especially under low lighting. By taking advantage of the Logarithmic Image Processing (LIP) context, we study two novel functional metrics: i) the ... More

Surface Groups In The Group Of Germs Of Analyticdiffeomorphisms In One VariableSep 04 2019We construct embeddings of surface groups into the group of germs of analytic diffeomorphisms in one variable.

On the inequalities in Hermite's theorem for a real polynomial to have real zerosSep 03 2019We prove expressions for the inequalities in Hermite's theorem which are conditions for a real polynomial to have real zeros. These expressions generalize the discriminant of a quadratic polynomial and the expression of J. Mar\'ik for a cubic polynomial. ... More

Tangential Loewner hullsSep 03 2019Through the Loewner equation, real-valued driving functions generate sets called Loewner hulls. We analyze driving functions that approach 0 at least as fast as $a (T-t)^r$ as $t \to T$, where $r \in (0, 1/2)$, and show that the corresponding Loewner ... More

Ax-Schanuel Type Theorems on Functional Transcendence via Nevanlinna TheorySep 03 2019We will apply Nevanlinna Theory to prove several Ax-Schanuel type Theorems for functional transcendence when the exponential map is replaced by other meromorphic functions. We also show that analytic dependence will imply algebraic dependence for certain ... More

Duality of boundary value problems for minimal and maximal surfacesSep 03 2019In 1966, Jenkins and Serrin gave existence and uniqueness results for infinite boundary value problems of minimal surfaces in the Euclidean space, and after that such solutions have been studied by using the univalent harmonic mapping theory. In this ... More

Duality of boundary value problems for minimal and maximal surfacesSep 03 2019Sep 09 2019In 1966, Jenkins and Serrin gave existence and uniqueness results for infinite boundary value problems of minimal surfaces in the Euclidean space, and after that such solutions have been studied by using the univalent harmonic mapping theory. In this ... More

The metric geometry of singularity typesSep 02 2019Let $X$ be a compact K\"ahler manifold. Given a big cohomology class $\{\theta\}$, there is a natural equivalence relation on the space of $\theta$-psh functions giving rise to $\mathcal S(X,\theta)$, the space of singularity types of potentials. We introduce ... More

Improved Bohr's phenomenon in quasi-subordination classesSep 02 2019Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and thereby we extend ... More

Punctured non-recurrent Siegel cylinders in automorphisms of $\mathbb{C}^{2}$Sep 02 2019We show the existence of automorphisms $F$ of $\mathbb{C}^{2}$ with a Fatou component $\Omega$ biholomorphic to $\mathbb{C}\times\mathbb{C}^{*}$ that is attracted to a Siegel curve (a curve on which $F$ is conjugated to an irrational rotation). We further ... More

Generalized Integration Operators on Hardy SpacesSep 02 2019We introduce a natural generalization of a well studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give simple proofs ... More

Combinatorially Determined Zeroes of Bernstein-Sato Ideals for Tame and Free ArrangementsSep 02 2019For a central, not necessarily reduced, hyperplane arrangement $f$, a factorization $f = f_{1} \cdots f_{r}$, and for $f^{\prime}$ dividing $f$, we consider the ideal of polynomials $B(S) \in \mathbb{C}[s_{1}, \dots, s_{r}]$ satisfying the functional ... More

Combinatorially Determined Zeroes of Bernstein--Sato Ideals for Tame and Free ArrangementsSep 02 2019Sep 06 2019For a central, not necessarily reduced, hyperplane arrangement $f$, a factorization $f = f_{1} \cdots f_{r}$, and for $f^{\prime}$ dividing $f$, we consider the ideal of polynomials $B(S) \in \mathbb{C}[s_{1}, \dots, s_{r}]$ satisfying the functional ... More

Quasi-squares of pseudocontinuable functionsSep 02 2019For an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\overline{H^p_0}$ be the associated star-invariant subspace of the Hardy space $H^p$. While the squaring operation $f\mapsto f^2$ maps $H^p$ into $H^{p/2}$, one cannot expect ... More

Quasi-squares of pseudocontinuable functionsSep 02 2019Sep 14 2019For an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\overline{H^p_0}$ be the associated star-invariant subspace of the Hardy space $H^p$. While the squaring operation $f\mapsto f^2$ maps $H^p$ into $H^{p/2}$, one cannot expect ... More

Hypercohomologies of truncated twisted holomorphic de Rham complexesSep 01 2019We investigate the hypercohomologies of truncated twisted holomorphic de Rham complexes on (not necessarily compact) complex manifolds. In particular, we generalize Leray-Hirsch, K\"{u}nneth and Poincar\'{e}-Serre duality theorems on them. At last, a ... More

Holomorphic sections of line bundles vanishing along subvarietiesSep 01 2019Let $X$ be a compact normal complex space of dimension $n$, and $L$ be a holomorphic line bundle on $X$. Suppose $\Sigma=(\Sigma_1,\ldots,\Sigma_\ell)$ is an $\ell$-tuple of distinct irreducible proper analytic subsets of $X$, $\tau=(\tau_1,\ldots,\tau_\ell)$ ... More

Construction of open up mappings with rational functions and related questionsAug 31 2019Using tools from algebraic geometry and the theory of Riemann surfaces, we establish the existence of special conformal mappings. Special emphasis is put on a constructive approach, and these mappings are rational functions with minimal degree. Three ... More

Functions with ultradifferentiable powersAug 31 2019We study the regularity of smooth functions $f$ defined on an open set of $\mathbb{R}^n$ and such that, for certain integers $p\geq 2$, the powers $f^p :x\mapsto (f(x))^p$ belong to a Denjoy-Carleman class $\mathcal{C}_M$ associated with a suitable weight ... More

Normality and Montel's TheoremAug 31 2019In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's normality test in ... More

A normality Criterion for a Family of Meromorphic FunctionsAug 31 2019Schwick, in [6], states that let $\mathcal{F}$ be a family of meromorphic functions on a domain $D$ and if for each $f\in\mathcal{F}$, $(f^n)^{(k)}\neq 1$, for $z\in D$, where $n, k$ are positive integers such that $n\geq k+3$, then $\mathcal{F}$ is a ... More

On a property of harmonic measure on simply connected domainsAug 30 2019Let $D \subset \mathbb{C}$ be a domain with $0 \in D$ and, for $R>0$, let ${{\hat \omega }_D}\left( {R} \right)$ denote the harmonic measure of $D \cap \left\{ {\left| z \right| = R} \right\}$ at $0$ and ${\omega _D}\left( {R} \right)$ denote the harmonic ... More

On the Hardy number of a domain in terms of harmonic measure and hyperbolic distanceAug 30 2019Let $\psi $ be a conformal map on $\mathbb{D}$ with $ \psi \left( 0 \right)=0$ and let ${F_\alpha }=\left\{ {z \in \mathbb{D}:\left| {\psi \left( z \right)} \right| = \alpha } \right\}$ for $\alpha >0$. Denote by ${H^p}\left( \mathbb{D} \right)$ the classical ... More

On a relation between harmonic measure and hyperbolic distance on planar domainsAug 30 2019Let $\psi $ be a conformal map of $\mathbb{D}$ onto an unbounded domain and, for $\alpha >0$, let ${F_\alpha }=\left\{ {z \in \mathbb{D}:\left| {\psi \left( z \right)} \right| = \alpha } \right\}$. If $\omega _\mathbb{D}\left( {0,{F_\alpha }} \right)$ ... More

Hyperbolic distance and membership of conformal maps in the Hardy spaceAug 30 2019Let $\psi$ be a conformal map of the unit disk $\mathbb{D}$ onto an unbounded domain and, for $\alpha >0$, let ${F_\alpha }=\left\{ {z \in \mathbb{D}:\left| {\psi \left( z \right)} \right| = \alpha } \right\}$. If ${H^p}\left( \mathbb{D} \right)$ denotes ... More

Nonproper intersection products and generalized cyclesAug 30 2019In this article we develop intersection theory in terms of the $\mathcal{B}$-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern ... More

Rigidity of flag supermanifoldsAug 30 2019We prove that under certain assumptions a supermanifold of flags is rigid, this is its complex structure does not admit any non-trivial small deformation. Moreover under the same assumptions we show that a supermanifold of flags is unique non-split supermanifold ... More

Integrability of difference equations with binomial seriesAug 30 2019We consider binomial series $\sum_{n=0}^\infty a_n z^{\underline{n}}$, where $z^{\underline{n}}=z(z-1)\cdots(z-n+1)$ in the complex plane. The order of growth can be obtained for some entire functions represented by binomial series. Integrability by binomial ... More

Infinitesimal CR automorphisms and stability groups of nonminimal infinite type models in $\mathbb C^2$Aug 30 2019We determine infinitesimal $\mathrm{CR}$ automorphisms and stability groups of real hypersurfaces in $\mathbb C^2$ in the case when the hypersurface is nonminimal and of infinite type at the reference point.

A Complete Realization of the orbits of generalized derivatives of Quasiregular MappingsAug 29 2019Quasiregular maps are differentiable almost everywhere maps which are analogous to holomorphic maps in the plane for higher real dimensions. Introduced by Gutlyanskii et al, the infinitesimal space is a generalization of the notion of derivatives for ... More

Quantifying the ill-conditioning of analytic continuationAug 29 2019Analytic continuation is ill-posed, but becomes merely ill-conditioned (although with an infinite condition number) if it is known that the function in question is bounded in a given region of the complex plane. In an annulus, the Hadamard three-circles ... More

Carleson embeddings for Hardy-Orlicz and Bergman-Orlicz spaces of the upper-half planeAug 29 2019In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper-half plane. We use these results to obtain embedding relations and pointwise multipliers between these spaces.

Bivariate poly-analytic Hermite polynomialsAug 28 2019A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical Hilbert space ... More

Critical Points, Critical Values, and a Determinant Identity for Complex PolynomialsAug 27 2019Given any n-tuple of complex numbers, one can canonically define a polynomial of degree n+1 that has the entries of this n-tuple as its critical points. In 2002, Beardon, Carne, and Ng studied a map $\theta\colon \mathbb{C}^n\to \mathbb{C}^n$ which outputs ... More

Poincarè- and Sobolev- type inequalities for complex $m$-Hessian equationsAug 27 2019By using quasi-Banach techniques as key ingredient we prove Poincar\`e- and Sobolev type inequalities for $m$-subharmonic functions with finite $(p,m)$-energy. We shall as well prove a partial result on the integrability of $m$-subharmonic functions.

On some geometric properties and Hardy class of q-Bessel functionsAug 27 2019In this paper, we deal with some geometric properties including starlikeness and convexity of order $\alpha$ of Jackson's second and third $q$-Bessel functions which are natural extensions of classical Bessel function $J_{\nu}$. In additon, we determine ... More

On some geometric properties and Hardy class of q-Bessel functionsAug 27 2019Sep 06 2019In this paper, we deal with some geometric properties including starlikeness and convexity of order $\alpha$ of Jackson's second and third $q$-Bessel functions which are natural extensions of classical Bessel function $J_{\nu}$. In additon, we determine ... More

Minimisers and Kellogg's theoremAug 27 2019Sep 11 2019We extend the celebrated theorem of Kellogg for conformal mappings to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimiser of Dirichlet energy of Sobolev mappings between double connected domains having $\mathscr{C}^{1,\alpha}$ ... More

Minimisers and Kellogg's theoremAug 27 2019We extend the celebrated theorem of Kellogg for conformal to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimiser of Dirichlet energy of Sobolev mappings between double connected domains having $\mathscr{C}^{n,\alpha}$ is ... More

Minimisers and Kellogg's theoremAug 27 2019Sep 05 2019We extend the celebrated theorem of Kellogg for conformal mappings to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimiser of Dirichlet energy of Sobolev mappings between double connected domains having $\mathscr{C}^{1,\alpha}$ ... More

Algebraic genericity of frequently universal harmonic functions on treesAug 26 2019We show that the set of frequently universal harmonic functions on a tree T contains a vector space except 0 which is dense in the space of harmonic functions on T seen as subset of C^T . In order to prove this we replace the complex plane C by any separable ... More

The asymptotic number of zeros of exponential sums in critical stripsAug 26 2019Normalized exponential sums are entire functions of the form $$ f(z)=1+H_1e^{w_1z}+\cdots+H_ne^{w_nz}, $$ where $H_1,\ldots, H_n\in\C$ and $0<w_1<\ldots<w_n$. It is known that the zeros of such functions are in finitely many vertical strips $S$. The asymptotic ... More

Veech groups and extended origamisAug 24 2019In this paper, we deal with flat surfaces of finite analytic type with two distinct Jenkins-Strebel directions. We show that such a flat surface is characterized by decomposition into parallelograms which consists of informations of angles, moduli, and ... More

The "pits effect" for entire functions of exponential type and the Wiener spectrumAug 24 2019Given a sequence $\xi\colon \mathbb Z_+ \to \mathbb C$, we find a simple spectral condition which guarantees the angular equidistribution of the zeroes of the Taylor series \[ F_\xi (z) = \sum_{n\ge 0} \xi (n) \frac{z^n}{n!}\,. \] This condition yields ... More

Pareto-optimal data compression for binary classification tasksAug 23 2019The goal of lossy data compression is to reduce the storage cost of a data set $X$ while retaining as much information as possible about something ($Y$) that you care about. For example, what aspects of an image $X$ contain the most information about ... More

Number and location of pre-images under harmonic mappings in the planeAug 23 2019We derive a formula for the number of pre-images under a non-degenerate harmonic mapping $f$, using the argument principle. This formula reveals a connection between the pre-images and the caustics. Moreover, our results allow to deduce the number of ... More

Hyperbolicity of coarse moduli spaces and isotriviality for certain familiesAug 22 2019In this paper, we prove the Kobayashi hyperbolicity of the coarse moduli spaces of canonically polarized or polarized Calabi-Yau manifolds in the sense of complex $V$-spaces (a generalization of complex $V$-manifolds in the sense of Satake). As an application, ... More

Holomorphic immersions of bi-disks into $9$ dimensional real hypersurfaces with Levi signature $(2, 2)$Aug 22 2019Inspired by an article of R. Bryant on holomorphic immersions of unit disks into Lorentzian CR manifolds, we discuss the application of Cartan's method to the question of the existence of bi-disk $\mathbb{D}^{2}$ in a smooth $9$-dimensional real analytic ... More

Classification of flat pencils of foliations on compact complex surfacesAug 22 2019Related to the classification of regular foliations in a complex algebraic surface, we address the problem of classifying the complex surfaces which admit a flat pencil of foliations. On this matter, a classification of flat pencils which admit foliations ... More

Teichmüller spaces of piecewise symmetric homeomorphisms on the unit circleAug 22 2019We interpolate a new family of Teichm\"uller spaces $T_{\sharp}^X$ between the universal Teichm\"uller space $T$ and its little subspace $T_0$, which we call the Teichm\"uller space of piecewise symmetric homeomorphisms. This is defined by prescribing ... More

Some estimation about Tayler-Maclaurin coefficients of generalized subclasses of bi-univalent functionsAug 21 2019Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of functions belonging ... More

The polarization constant of finite dimensional complex spaces is oneAug 21 2019The polarization constant of a Banach space $X$ is defined as $$\mathbf c(X):= \limsup\limits_{k\rightarrow \infty} \mathbf c(k, X)^\frac{1}{k},$$ where $\mathbf c(k, X)$ stands for the best constant $C>0$ such that $ \Vert \overset{\vee}{P} \Vert \leq ... More

Non-negativity of CR Paneitz operator for embeddable CR manifoldsAug 21 2019The non-negativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this non-negativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe ... More

Algebraic relations between moments of plane polygonsAug 20 2019We describe the algebraic relations satisfied by the harmonic and anti-harmonic moments of simply connected, but not necessarily convex planar polygons with a given number of vertices.