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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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Groups of linear isometries of spaces M q of holomorphic functions of several complex variables [PDF]
Mathematical Notes, 2008 C n = {z = (z1, z2, . . . , zn) | zk ∈ C, 1 ≤ k ≤ n} be the standard n-dimensional complex coordinate space. ByG we denote the ball Bn = {z ∈ C | |z1| + |z2| + · · ·+ |zn| < 1} or the polydisk U = {z ∈ C | |z1| < 1, . . . , |zn| < 1} in the space Cn, and by Γ we denote the Bergman–Shilov boundary of G: ifG = Bn, then we take Γ = Sn = {z ∈ C | |z1| + · ·
A. V. Subbotin
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Algebras of symmetric holomorphic functions of several complex variables
Revista Matemática Complutense, 2018Given a proper holomorphic mapping $$g:\varOmega \subseteq {\mathbb {C}}^{n}\longrightarrow \varOmega ' \subseteq {\mathbb {C}}^{n}$$ and an algebra of holomorphic functions
R. Aron +3 more
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Boundary Morera theorems for holomorphic functions of several complex variables
Duke Mathematical Journal, 1991 Sei \(D\subset\mathbb{C}^ N\) ein beschränktes Gebiet und \(A(D):=C(\overline D)\cap{\mathcal O}(D)\). In der Arbeit geht es um die Frage, wann eine Funktion \(f\in C(\partial D)\) nach \(D\) holomorph fortsetzbar, d.h. Beschränkung einer Funktion aus \(A(D)\) ist. Eine notwendige und unter geeigneten Voraussetzungen auch hinreichende Bedingung ist die
J. Globevnik, E. L. Stout
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On holomorphic operator-functions of several complex variables
Functional Analysis and Its Applications, 1970 S. G. Kreĭn, V. P. Trofimov
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Boundary behavior of holomorphic functions of several complex variables
Mathematical Notes of the Academy of Sciences of the USSR, 1986The 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 ...
P. V. Dovbush
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The Riemann-Hilbert boundary-value problem for holomorphic functions of several complex variables
Ukrainian Mathematical Journal, 1969 М. А. Бородин
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The convergence of Pade´-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.
N. Daras
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