Results 21 to 30 of about 1,046,218 (306)
Axioms, 2023 The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed.
Tamara Antonova +3 more
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Kernel convergence and biholomorphic mappings in several complex variables
International Journal of Mathematics and Mathematical Sciences, 2003 We deal with kernel convergence of domains in ℂn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem,
Gabriela Kohr
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On Pólya’s Theorem in several complex variables [PDF]
Banach Center Publications, 2015 Let $K$ be a compact set in $\mathbb{C}$, $f$ a function analytic in $\overline{\mathbb{C}}\smallsetminus K$ vanishing at $\infty $. Let $% f\left( z\right) =\sum_{k=0}^{\infty }a_{k}\ z^{-k-1}$ be its Taylor expansion at $\infty $, and $H_{s}\left( f\right) =\det \left( a_{k+l}\right) _{k,l=0}^{s}$ the sequence of Hankel determinants.
Günyüz, Ozan, Zakharyuta, Vyacheslav
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Representation of logarithm of entire function in several complex variables
Karpatsʹkì Matematičnì Publìkacìï, 2013 The integral representation of some branch of an entire on $\mathbb{C}^n$ function which generalized the Poisson-Jensen-Stoll Formula is obtained.
O. Ya. Brodyak, Ya. V. Vasyl'kiv
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The *-product of domains in several complex variables
Complex Variables and Elliptic Equations, 2022 In this article we continue the research, carried out in \cite{zajac}, on computing the $*$-product of domains in $\CC^N$. Assuming that $0\in G\subset\CC^N$ is an arbitrary Runge domain and $0\in D\subset\CC^N$ is a bounded, smooth and linearly convex domain (or a non-decreasing union of such ones), we establish a geometric relation between $D*G$ and ...
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k-convexity in several complex variables [PDF]
Annales Polonici Mathematici, 2002 Formerly, D.~Mejia, D.~Minda and W.~Ma investigated the hyperbolic geometry of \(k\)-convex regions in \(\mathbb C\), \(k\)-convex functions on the unit disk \(U \in \mathbb C\), and obtained growth and distortion theorems for \(k\)-convex functions on \(U\). In this paper, their results are generalized for the case of several complex variables.
Hamada, Hidetaka, Kohr, Gabriela
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Bloch functions of several complex variables [PDF]
Pacific Journal of Mathematics, 1992 The author presents various properties of the Bloch mappings \(f:\mathbb{B}\to\mathbb{C}^ n\), where \(\mathbb{B}\) denotes the unit Euclidean ball in \(\mathbb{C}^ n\). In particular, he proves the following results. Let \(f\) be a holomorphic mapping \(\mathbb{B}\to\mathbb{C}^ n\) and let \[ \| f\|_ B:=\sup\{\|(f\circ\varphi)'(0)\|:\;\varphi\in\text ...
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A Note on Strongly Starlike Mappings in Several Complex Variables
Abstract and Applied Analysis, 2014 Let f be a normalized biholomorphic mapping on the Euclidean unit ball 𝔹n in ℂn and let α∈0,1. In this paper, we will show that if f is strongly starlike of order α in the sense of Liczberski and Starkov, then it is also strongly starlike of order α in ...
Hidetaka Hamada +3 more
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Journal of Mathematics, 2023 This article is to describe the entire solutions of some partial differential-difference equations and systems. Some theorems about the forms of transcendental entire solutions with finite order for several high-order partial differential-difference ...
Yuxian Chen, Libing Xie, Hongyan Xu
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Prescribing the preSchwarzian in several complex variables
Annales Academiae Scientiarum Fennicae Mathematica, 2011 We solve the several complex variables preSchwarzian operator equation $[Df(z)]^{-1}D^2f(z)=A(z)$, $z\in \C^n$, where $A(z)$ is a bilinear operator and $f$ is a $\C^n$ valued locally biholomorphic function on a domain in $\C^n$. Then one can define a several variables $f\to f_α$ transform via the operator equation $[Df_α(z)]^{-1}D^2f_α(z)=α[Df(z)]^{-1 ...
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