Results 121 to 130 of about 28,571 (151)

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;
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Boundary behavior of holomorphic functions of several complex variables

Mathematical Notes of the Academy of Sciences of the USSR, 1986
The author generalizes for strictly pseudoconvex domains \(D\subset {\mathbb{C}}^ n\), \textit{W. Seidel}'s [Trans. Am. Math. Soc. 34, 1-21 (1932)] criterium of equality of the limit of two sequences of values \(f(a_ m)\), \(f(b_ m)\) \((m=1,2,...)\) of a bounded holomorphic function f defined on the unit disc \(U\subset {\mathbb{C}}\), when the ...
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k-holomorphic functions in spaces of several complex variables

Complex Variables and Elliptic Equations, 2019
In this paper, we define k-holomorphic functions in Cn and study their properties. We obtain some conclusions parallel to the properties of holomorphic functions, such as Cauchy integral theorem, C...
Yuying Qiao, Yanyan Cui, Zunfeng Li, Liping Wang   +3 more
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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 ...
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Some boundary properties of holomorphic functions of several complex variables

Mathematical Notes of the Academy of Sciences of the USSR, 1978
A local uniqueness theorem and analogs of the theorem on removable singularities under the hypothesis of boundedness are proved for functions satisfying the tangential Cauchy-Riemann conditions on hypersurfaces in Cn. The results can be interpreted as giving certain boundary properties of holomorphic functions of several complex variables.
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HOLOMORPHIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES WITH NONNEGATIVE REAL PART. TRACES OF HOLOMORPHIC AND PLURIHARMONIC FUNCTIONS ON THE ŠILOV BOUNDARY

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.
Ajzenberg, L. A., Dautov, S. A.
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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.
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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 ...
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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.
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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
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