Latest in math.cv
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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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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