Holomorphic extension from the sphere to the ball in Hilbert space
J. A. Cima, J. A. Pfaltzgraff (1983)
Annales Polonici Mathematici
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Displaying similar documents to “A continuation theorem for holomorphic mapping into a Hilbert space”
Holomorphic extension from the sphere to the ball in Hilbert space
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Annales Polonici Mathematici
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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,...
Proper holomorphic self-mappings of the symmetrized bidisc
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Annales Polonici Mathematici
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We characterize proper holomorphic self-mappings 𝔾₂ → 𝔾₂ for the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂): |λ₁|,|λ₂| < 1} ⊂ ℂ².
Recent developments in the theory of separately holomorphic mappings
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We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.
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We study a linearization of a real-analytic plane map in the neighborhood of its fixed point of holomorphic type. We prove a generalization of the classical Koenig theorem. To do that, we use the well known results concerning the local dynamics of holomorphic mappings in ℂ².
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A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions
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;...