Results 11 to 20 of about 519 (182)
Bounded Holomorphic Functions of Several Complex Variables. I [PDF]
Transactions of the American Mathematical Society, 1971 A domain of bounded holomorphy in a complex analytic manifold is a maximal domain for which every bounded holomorphic function has a bounded analytic continuation. In this paper, we show that this is a local property: if, for each boundary point of a domain, there exists a bounded holomorphic function which cannot be continued to any neighborhood of ...
Dong Sie Kim
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Inequalities for holomorphic functions of several complex variables [PDF]
Transactions of the American Mathematical Society, 1983 Sharp norm-inequalities, valid for functional Hilbert spaces of holomorphic functions on the polydisk, unit ball and
Jacob Burbea
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A Removability Result for Holomorphic Functions of Several Complex Variables
Journal of Basic & Applied Sciences, 2016 Suppose that Ω is a domain of Cn, n > 1, E ⊂ Ω closed in W, the Hausdorff measure H2n-1(E)=0, and f is holomorphic in Ω/E. It is a classical result of Besicovitch that if n = 1 and f is bounded, then f has a unique holomorphic extension to Ω.
Juhani Riihentaus
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Removable sets for holomorphic functions of several complex variables [PDF]
Publicacions Matemàtiques, 1989 We show that every closed subset of CN that has finite (2N-2) dimensional measure is a removable set for holomorphic functions, and we obtain a related result on the ball.
Stout, Edgar Lee, E. Lee Stout
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Slice Holomorphic Functions in Several Variables with Bounded L-Index in Direction
Axioms, 2019 In this paper, for a given direction b ∈ C n \ { 0 } we investigate slice entire functions of several complex variables, i.e., we consider functions which are entire on a complex line { z 0 + t b : t ∈ C } for any z
Andriy Bandura, Oleh Skaskiv
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Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables [PDF]
Ukrainian Mathematical Bulletin, 2019 We investigate the slice holomorphic functions of several complex variables that have a bounded \(L\)-index in some direction and are entire on every slice \(\{z^0+t\mathbf{b}: t\in\mathbb{C}\}\) for every \(z^0\in\mathbb{C}^n\) and for a given direction \(\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}\).
Bandura, A., Skaskiv, O.
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New properties of some families of holomorphic functions of several complex variables
Demonstratio Mathematica, 2009 AbstractThe paper concerns holomorphic functions in complete ...
Edyta Leś-Bomba, Piotr Liczberski
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Journal of Mathematical Analysis and Applications, 2001 Bohr's theorem [\textit{H. Bohr}, Proc. Lond. Math. Soc. (2) 13, 1-5 (1914; JFM 44.0289.01)] states that given an analytic function in the unit disk, \(f(z) = \sum_k c_k z^k\), such that \(|f(z)|< 1\) for any \(z\) in the disk, then \(\sum_k |c_k z^k|0\), and a compact set \(K\) such that \(\|f\|_U \leq C |f|_K\), for all bounded holomorphic \(f\).
Aizenberg, Lev +2 more
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Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
Discrete Analysis, 2023 Bi-parameter potential theory and Carleson measures for the Dirichlet space on the bidisc, Discrete Analysis 2023:22, 58 pp. Carleson measures arise naturally when considering harmonic or holomorphic extensions from the boundary of a domain to the ...
Nicola Arcozzi +3 more
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Slice Holomorphic Functions in the Unit Ball Having a Bounded L-Index in Direction
Axioms, 2020 Let b∈Cn\{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e., we study functions that are analytic in the intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12 ...
Andriy Bandura +2 more
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