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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A Removability Result for Holomorphic Functions of Several Complex Variables [PDF]
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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Banach Spaces of Analytic Vector-valued Functions [PDF]
, 2007 The main theme of the thesis is the study of continuity and approximation problems, involving matrix-valued and vector-valued Hardy spaces on the unit disc ID and its boundary T in the complex plane.
Barclay, Steven John
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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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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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The star function for meromorphic functions of several complex variables [PDF]
, 2019 We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f. We then characterize meromorphic
Abi-Khuzam, Faruk F. +2 more
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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
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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
Globevnik, Josip, Stout, Edgar Lee
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Lipschitz-Type and Bloch-Type Spaces of Pluriharmonic Mappings in a Hilbert Space
Journal of Function Spaces, 2017 We investigate some properties of pluriharmonic mappings in an infinite dimensional complex Hilbert space. Several characterizations for pluriharmonic mappings to be in Lipschitz-type and Bloch-type spaces are given, which are generalizations of the ...
Yong Liu
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