Results 111 to 120 of about 347 (160)
Algebras of symmetric holomorphic functions of several complex variables
Revista Matemática Complutense, 2018 Let \(g:\Omega\longrightarrow\Omega'\) be a proper holomorphic mapping, where \(\Omega\subset\mathbb C^n\), \(\Omega'\subset\mathbb C^k\), \(k\geq n\). Given an algebra \(\mathcal B(U)\) of functions defined on a set \(U\subset\Omega\) (e.g., \(\mathcal P(K)\), \(\mathcal O(U)\), \(\mathcal A(U)\), \(\mathcal H^\infty(U)\)) the authors study properties
Richard M. Aron +3 more
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Distortion Properties of Holomorphic Functions of Several Complex Variables
Mathematische Nachrichten, 1980 Let Q(D) be a class of functions q, q(0) = 0, |q(z)| < 1 holomorphic in the Reinhardt domain D ⊂ Cn, a and b — arbitrary fixed numbers satisfying the condition — 1 ≤ b < a ≤ 1. 𝔭(a, b; D) — the class of functions p such that p ϵ 𝔭(a, b; D) iff for some q ϵ Q(D) and every z ϵ D. S*(a, b; D) — the class of functions f such that f ϵ S*(a, g;
Ryszard Mazur
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Embedding theorems for holomorphic functions of several complex variables
Journal of Applied Analysis, 2013 Summary: Many authors studied families \(\mathcal X_{\mathcal G}\) of complex valued functions, which are holomorphic in bounded complete \(n\)-circular domains \(\mathcal G \subset \mathbb C^n\) and fulfil some geometric conditions. The above functions were applied later to study families of locally biholomorphic mappings in \(\mathbb C^{n}\). In this
Renata Długosz
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Admissible limits of normal holomorphic functions of several complex variables
Mathematical Notes of the Academy of Sciences of the USSR, 1990 Let \(D\subset {\mathbb{C}}^ n\) (n\(\geq 2)\) be a domain with \(C^ 2\)- boundary. We say that a function \(f\in {\mathcal O}(D)\) is normal if there exists a constant M such that \({\mathcal L}_{\log (1+| f|^ 2)}(z;v)\leq M\kappa_ D(z;v)\), \(z\in D\), \(v\in {\mathbb{C}}^ n\), where \({\mathcal L}\) denotes the Levi form and \(\kappa_ D\) is the ...
P. V. Dovbush
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The convergence of Padé-type approximants to holomorphic functions of several complex variables
Applied Numerical Mathematics, 1990 The author proves two generalizations of \textit{M. Eiermann's} [J. Comput. Appl. Math. 10, 219-227 (1984; Zbl 0538.65011)] sufficient condition for linear summability of power series, one where the summation method is applied to partial sums of the multidimensional power series and one where different summation matrices are used in different variables.
Nicholas J. Daras
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Mathematics of the USSR-Sbornik, 1976 For a certain class of domains, conditions are given which a continuous function on the Silov boundary of a domain must satisfy in order that there exist a holomorphic (pluriharmonic) function in , continuous on and such that . Bibliography: 24 titles.
Lev Aizenberg, Sh. A. Dautov
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A boundary uniqueness theorem for holomorphic functions of several complex variables
Mathematical Notes of the Academy of Sciences of the USSR, 1974 If D ⊂ Cn is a region with a smooth boundary and M ⊂ ∂D is a smooth manifold such that for some point p ∈ M the complex linear hull of the tangent plane Tp(M) coincides with Cn, then for each functionf e A(D) the conditionf¦M=0 implies thatf=0 in D.
S. I. Pinehuk
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Groups of linear isometries of spaces M q of holomorphic functions of several complex variables
Mathematical Notes, 2008 Let \(G\) be the unit ball or the unit polydisk in \(\mathbb C^n\) and \(\Gamma\) be the Bergman-Shilov boundary of \(G\). Let \(M^q\) be the class of all holomorphic functions \(f\) in \(G\) such that \[ \int \limits_{\Gamma} (\ln^+ \{\sup \limits_{0 \leq r < 1} |f (r \zeta)|)^q \sigma (d \zeta) < + \infty, \] where \(\sigma\) is an invariant ...
A. V. Subbotin
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I Elementary local properties of holomorphic functions of several complex variables
, 2010 In this chapter we study the local properties of holomorphic functions of several complex variables which can be deduced directly from the classical theory of holomorphic functions in one complex variable. The basis for our work is a Cauchy formula for polydiscs which generalises the classical Cauchy formula. Most of the theorems proved in this chapter
Christine Laurent‐Thiébaut
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Extensions of p-Yosida functions to holomorphic mappings of several complex variables
Complex Variables and Elliptic Equations, 2019 Let M be a complete complex Hermitian manifold with metric EM. A holomorphic mapping f:Cm→M is called p-Yosida mapping if ∥z∥2−pEM(f(z),df(z)(ξ)) is bounded above for z,ξ∈Cm with ∥ξ∥=1, where df(z)...
Liu Yang
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