复变函数

Let $X$ be a complex manifold $X$ of dimension $k,$ and let $V\subset X$ be a K\"ahler submanifold of dimension $l,$ and let $B\subset V$ be a piecewise $\mathcal{C}^2$-smooth domain. Let $T$ be a positive closed currents of bidegree…

We study the dynamics of Stirling's iterative root-finding method $St_f(z)$ for rational and polynomial functions. It is seen that the Scaling theorem is not satisfied by Stirling's iterative root-finding method. We prove that for a…

The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…

We study conditions so that the determinantal point process $\Lambda_\phi$ associated to a generalized Fock space defined by a doubling subharmonic weight $\phi$ is almost surely a separated sequence in $\mathbb C$. Under a natural…

A rational lemniscate is a level set of $|r|$ where $r: \hat{\mathbb{C}} \rightarrow \hat{\mathbb{C}}$ is rational. We prove that any planar Euler graph can be approximated, in a strong sense, by a homeomorphic rational lemniscate. This…

Results providing conditions on a family of integro-differential operators to determine a formal automorphism are established. Equivalently, the problem can be read in terms of existence and uniqueness of formal solutions of Cauchy problems…

In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay…

We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…

We prove that singularities with holomorphic monodromies are preserved by the Hadamard product. We find an explicit formula for the monodromy of the singularities, and similar formulas for the exponential e\~ne product. Using these formulas…

We will consider first-order difference equations of the form \[ y(z+1) = \frac{\lambda y(z)+a_2(z)y(z)^2+\cdots+a_p(z)y(z)^p}{1 + b_1(z)y(z)+\cdots+b_q(z)y(z)^q}, \] where $\lambda\in\mathbb{C}\setminus\{0\}$ and the coefficients $a_j(z)$…

We study small eigenvalues of Toeplitz operators on polarized complex projective manifolds. For Toeplitz operators whose symbols are supported on proper subsets, we prove the existence of eigenvalues that decay exponentially with respect to…

Let $X$ be a compact K\"ahler manifold whose anticanonical cohomology class is semipositive. Let $L$ be a big and semi-ample line bundle on $X$ and $\alpha$ be the Chern class of $L$. We give a sufficient condition ensuring that the…

Suppose $V$ is a singular complex analytic curve inside $\mathbb{C}^{2}$. We investigate when a singular or non-singular complex analytic curve $W$ inside $\mathbb{C}^{2}$ with sufficiently small Hausdorff distance $d_{H}(V, W)$ from $V$…

In this paper, we have found that some certain Fermat-type shift and difference equations have the meromorphic solutions generated by Riccati type functions. Also we have solved the open problems posed by Liu and Yang (A note on meromorphic…

It is crucial to explore the sharp bounds of logarithmic coefficients and the Hankel determinant involving logarithmic coefficients as part of coefficient problems in various function classes. Our primary objective in this study is to…

In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.

In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.

In this paper, we study a Dirichlet type problem for the non-pluripolar complex Monge - Amp\`ere equation with prescribed singularity on a bounded domain of $\mathbb{C}^n$. We provide a local version for an existence and uniqueness theorem…

Let $M$ be an open Riemann surface and $A$ be the punctured cone in $\mathbb{C}^n\setminus\{0\}$ on a smooth projective variety $Y$ in $\mathbb{P}^{n-1}$. Recently, Runge approximation theorems with interpolation for holomorphic immersions…

Number states and thermal states form an important class of physical states in quantum theory. A mathematical framework for studying these states is that of a Fock space over an appropriate Hilbert space. Several generalizations of the…