On some properties of a differential operator on the polydisk.
Shamoyan, Romi, Li, Songxiao (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Shamoyan, Romi, Li, Songxiao (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Ludwik M. Drużkowski (1983)
Annales Polonici Mathematici
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Peter Pflug (2003)
Annales Polonici Mathematici
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This note is an attempt to describe a part of the historical development of the research on separately holomorphic functions.
Ludwik M. Drużkowski (1980)
Annales Polonici Mathematici
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M. Nikić (1988)
Matematički Vesnik
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Armen Edigarian, Said El Marzguioui, Jan Wiegerinck (2010)
Annales Polonici Mathematici
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We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.
Alexander V. Abanin, Pham Trong Tien (2013)
Studia Mathematica
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Anahit Harutyunyan, Wolfgang Lusky (2008)
Studia Mathematica
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We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
M. Mateljević (1986)
Matematički Vesnik
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Joji Kajiwara (1974)
Czechoslovak Mathematical Journal
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P. Pflug (1985)
Matematički Vesnik
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Alexander V. Abanin, Pham Trong Tien (2012)
Studia Mathematica
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We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional. ...
Christopher Boyd, Pilar Rueda (2009)
Studia Mathematica
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We study isometries between spaces of weighted holomorphic functions. We show that such isometries have a canonical form determined by a group of homeomorphisms of a distinguished subset of the range and domain. A number of invariants for these isometries are determined. For specific families of weights we classify the form isometries can take.
Maciej P. Denkowski (2007)
Annales Polonici Mathematici
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We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection,...
Marek Jarnicki
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CONTENTS§1. Introduction.................................................................................................................5§2. Basic properties of δ-tempered holomorphic functions...............................................8§3. Holomorphic continuation and holomorphic retractions.............................................20§4. Continuation from regular neighbourhoods...............................................................32§5. Continuation from δ-regular submanifolds;...
Takeo Ohsawa (1995)
Mathematische Zeitschrift
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