S. Favorov
We give necessary and sufficient conditions for a divisor in a tube domain to be the divisor of a holomorphic function with almost--periodic modulus.
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On positive semi-definite holomorphic sectional curvature with many zeroes
该研究在自然几何背景下证明了带大量零点的半正全纯截面曲率的完备Kähler度量的存在性，用Koiso-Sakane形式的Calabi Ansatz在射影直线 tautological 线丛幂的全空间上构造了此类度量，还提出紧情形猜想并得到非紧情形类似结果。
It is known that the Cauchy's argument principle, applied to an holomorphic function $f$, requires that $f$ has no zeros on the curve of integration. In this short note, we give a generalization of such a principle which covers the case when $f$ has zeros on the curve, as well as an application.
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings between the unit balls in complex spaces. This extends the classical Schwarz-Pick lemma and the related result proved by Pavlovic.
We prove a local Nullstellensatz with parameter for a continuous family of c-holomorphic functions with an effective exponent independent of the parameter: the local degree of the cycle of zeroes of the central section section. We assume that this central section defines a proper intersection and we show that we can omit this assumption in case of isolated zeroes.
Equivalent Bergman Spaces with Inequivalent Weights
该研究证明每个加权平方可积全纯函数空间都存在使Bergman核有零点的等价权重，还给出了一族对应Bergman核有无穷多零点的$L^1(\u2102)$径向权重，丰富了Bergman空间与权重关系的理论。
In this paper, we establish Lipschitz conditions for the norm of holomorphic mappings between the unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$ and $X,$ a complex normed space. This extends the work of Djordjević and Pavlović.
Locally approximable CR functions, a sharp maximum modulus principle and holomorphic extension
本文提出约化复空间局部闭子集上的局部可逼近连续 CR 函数概念，并在弱伪凹条件下建立最优最大模原理，同时将 CR 子流形的全纯延拓结果推广到含 CR 奇点的实子流形。
Kalantari's Geometric Modulus Principle describes the local behavior of the modulus of a polynomial. Specifically, if $p(z) = a_0 + \sum_{j=k}^n a_j\left(z-z_0\right)^j,\;a_0a_ka_n \neq 0$, then the complex plane near $z = z_0$ comprises $2k$ sectors of angle $\fracπ{k}$, alternating between arguments of ascent (angles $θ$ where $|p(z_0 + te^{iθ})| > |p(z_0)|$ for small $t$) and arguments of descent (where the opposite inequality holds). In this paper, we generalize the Geometric Modulus Principle to holomorphic and harmonic functions. As in Kalantari's original paper, we use these extensions …
Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems
本文研究交错实 *-代数上的切片正则函数，证明可在适当子集上指定零点与函数值，并由此得出轴对称域上存在不可延拓的此类函数。
Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a Kähler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the hyperbolic distance on $(-1,1)$ inhered from the domain $(-1,1)\times\mathbb{R}$. Moreover, in the case of bounded holomorphic functions we prove that the modulus is contractive with respect to the distance on the manifold and the hyperbolic distance on the unit disk.
Let $u$ be a plurisubharmonic function. We prove the existence of a nonzero holomorphic function such that the logarithm of its modulus is not more than local averages of this function $u$. This is the abstract for scientific conference "Algebra, Analysis and Related Problems of Mathematical Modeling" (Vladikavkaz, June 26-27, 2015) dedicated to the 60th anniversary of Professor, Doctor of Physical and Mathematical Sciences Vladimir A. Koibaev
Classic complex analysis is built on structural function $K=1$ only associated with Cauchy-Riemann equations, subsequently various generalizations of Cauchy-Riemann equations start to break this situation. The goal of this article is to show that only structural function $K=Const$ such that Liouville's theorem is held, otherwise, it's not valid any more on complex domain based on structural holomorphic, the correction should be $w=Φ{{e}^{-K}}$, where $Φ=Const$. Those theories in complex analysis which keep constant are unable to be held as constant in the framework of structural holomorphic. S…
This paper is concerned with the distribution of normalized zero-sets of random entire functions. The normalization of the zero-set is performed in the same way as that of the counting function for an entire function in Nevanlinna theory. The result generalizes the Shiffman and Zelditch theory on the distribution of the zeroes of random holomorphic sections of powers for positive Hermitian holomorphic line bundles from polynomial functions to entire functions. Our result can also be viewed as the analogy of Nevanlinna's First Main Theorem in the theory of the distribution of zero-sets of rando…
Few remarks on the Poincaré metric on a singular holomorphic foliation
本文研究奇异全纯叶状结构上Verjovsky均匀化映射模量在Carathéodory核意义下随定义域变化时的连续性，受Lins Neto--Martins工作启发。
We consider a family E_m(D,M) of holomorphic bundles constructed as follows: to any given M in GL_n(Z), we associate a "multiplicative automorphism" f of (C*)^n. Now let D be a f-invariant Stein Reinhardt domain in (C*)^n. Then E_m(D,M) is defined as the flat bundle over the annulus of modulus m>0, with fiber D, and monodromy f. We show that the function theory on E_m(D,M) depends nontrivially on the parameters m, M and D. Our main result is that E_m(D,M) is Stein if and only if m log(r(M)) <= 2 π^2, where r(M) denotes the max of the spectral radii of M and its inverse. As corollaries, we: -- …
Models of holomorphic functions on the symmetrized skew bidisc
本文研究对称化斜双曲盘上模不超过1的全纯函数理论，提出函数的实现公式和模型公式。
We investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic fixed point under analytic conjugacy. We then study some geometric applications: existence of real analytic invariant curve, existence of holomorphic and antiholomorphic roots of holomorphic and antiholomorphic parabolic germs, commuting holomorphic and antiholomorphic parabolic germs.
We study functions f(z) holomorphic in the upper half plane and having no zeros when the imaginary part of z is between 0 and 1, and we obtain a lower bound for the modulus of f(z) in this strip. In our analysis we deal with scalar functions f(z) as well as with operator valued holomorphic functions I+A(z) assuming that A(z) is a trace class operator in the upper half plane and I+A(z) is invertible in the same strip and is unitary on the real line.
We provide results of uniqueness for holomorphic functions in the Nevanlinna class bridging those previously obtained by Hayman and Lyubarskii-Seip. Namely, we propose certain classes of hyperbolically separated sequences in the disk, in terms of the rate of non-tangential accumulation to the boundary (the endpoints of this spectrum of classes being respectively the sequences with a non-tangential cluster set of positive measure, and the sequences violating the Blaschke condition); and for each of those classes, we give a critical condition of radial decrease on the modulus which will force a …
By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of $n$-best kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for the corresponding class of Bochner type spaces of stochastic processes. This study thus generalizes the classical result of $n$-best rational approximation for the Hardy space and a recent result of $n$-best kernel approximation for the weighted Bergman spaces of the unit disc. The type of approximations have significant applications to signal and image proce…
We give a new, simple proof of the fact recently discovered by C.-S. Lin and C.-L. Wang that the Green function of a torus has either three or five critical points, depending on the modulus of the torus. The proof uses anti-holomorphic dynamics. As a byproduct we find a one-parametric family of anti-holomorphic dynamical systems for which the parameter space consists only of hyperbolic components and analytic curves separating them.
Holomorphic Interpolation of Multivariate Completely Monotone Functions
通过将完全单调函数表示为正测度的Laplace或Stieltjes-Fantappiè变换，利用非交换Radon变换框架结合矩阵束实现与Weyl运算微积，实现有限点插值，得到方向完全单调的整函数或有理函数。
Let $f$ be a holomorphic function on the strip $\{z\in C: -α<Im z<α\}, α> 0$, belonging to the class $H(α,-α;ε)$ defined below. It is shown that there exist holomorphic functions $w_1$ on $\{z\in C: 0<Im z <2 α\}$ and $w_2$ on $\{z\in C: -2 α<Im z<2 α\}$ such that $w_1$ and $w_2$ have boundary values of modulus one on the real axis and satisfy the relation $w_1(z)=f(z-αi)w_2(z-2 αi)$ and $w_2(z+2 αi)= \bar{f}(z+αi)w_1(z)$ for $0<Im z<2$, where $\bar{f}(z):=\bar{f(\bar{z})}$. This leads to a "polar decomposition" $f(z)=u_f(z+αi)g_f(z)$ of the function $f(z)$, where $u_f(z+αi)$ and $g_f(z)$ are …
The main goal of this work is to give new and precise generalizations to various classes of plurisubharmonic functions of the classical minimum modulus principle for holomorphic functions of one complex variable, in the spirit of the famous lemma of Cartan-Boutroux. As an application we obtain precise estimates on the size of "plurisubharmonic lemniscates" in terms of appropriate Hausdorff contents.
Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.
Sharp Bohr-Rogosinski radii for Schwarz functions and Euler operators in C^n
本文研究了多复变量中Schwarz函数和Euler算子的锐Bohr-Rogosinski半径，通过多维Bohr不等式推广和导数估计，确定了最优半径并验证了其锐性。
Given a domain $D$ in $\mathbb{C}^n$ and $K$ a compact subset of $D$, the set $\mathcal{A}_K^D$ of all restrictions of functions holomorphic on $D$ the modulus of which is bounded by $1$ is a compact subset of the Banach space $C(K)$ of continuous functions on $K$. The sequence $(d_m(\mathcal{A}_K^D))_{m\in \mathbb{N}}$ of Kolmogorov $m$-widths of $\mathcal{A}_K^D$ provides a measure of the degree of compactness of the set $\mathcal{A}_K^D$ in $C(K)$ and the study of its asymptotics has a long history, essentially going back to Kolmogorov's work on $ε$-entropy of compact sets in the 1950s. In …
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