Results 151 to 160 of about 519 (182)
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Some boundary properties of holomorphic functions of several complex variables
Mathematical Notes of the Academy of Sciences of the USSR, 1978A 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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Admissible limits of normal holomorphic functions of several complex variables
Mathematical Notes of the Academy of Sciences of the USSR, 1990Let \(D\subset {\mathbb{C}}^ n\) (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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Chinese Annals of Mathematics, Series B, 2023
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Mathematica Slovaca
Abstract The paper is devoted to two new versions of Jack’s lemma for holomorphic functions of several complex variables. The assumption in the first case are formulated in the terms of the real part of certain complex quantities related to Jack’s lemma, and in the second one in the terms of the argument of adequate quantities.
Renata Długosz, Edyta Trybucka
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Abstract The paper is devoted to two new versions of Jack’s lemma for holomorphic functions of several complex variables. The assumption in the first case are formulated in the terms of the real part of certain complex quantities related to Jack’s lemma, and in the second one in the terms of the argument of adequate quantities.
Renata Długosz, Edyta Trybucka
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The convergence of Padé-type approximants to holomorphic functions of several complex variables
Applied Numerical Mathematics, 1990The 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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Groups of linear isometries of spaces M q of holomorphic functions of several complex variables
Mathematical Notes, 2008Let \(G\) 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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On holomorphic operator-functions of several complex variables
Functional Analysis and Its Applications, 1969Kreĭn, S. G., Trofimov, V. P.
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I Elementary local properties of holomorphic functions of several complex variables
2010In 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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k-holomorphic functions in spaces of several complex variables
Complex Variables and Elliptic Equations, 2020Yuying Qiao, Zunfeng Li
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Some properties of holomorphic Cliffordian functions in complex Clifford analysis
Acta Mathematica Scientia, 2010Ku Min, Du Jinyuan, Wang Daoshun
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