On Analytic Interpolation Manifolds in Boundaries of Weakly Pseudoconvex Domains

DOI10.1080/02781070290034593zbMATH Open1038.32007arXivmath/0106182OpenAlexW2044365065MaRDI QIDQ4433218

Gautam Bharali

Publication date: 2002

Published in: Complex Variables, Theory and Application: An International Journal (Search for Journal in Brave)

Abstract: Let $Omega$ be a bounded, weakly pseudoconvex domain in C^n, n > 1, with real-analytic boundary. A real-analytic submanifold $MsubsetbdOmega$ is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to $$. We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of $bdOmega$.

Full work available at URL: https://arxiv.org/abs/math/0106182

zbMATH Keywords

pseudoconvex domainfinite type domaininterpolation setcomplex-tangential

Mathematics Subject Classification ID

Analytic continuation (32D99) Finite-type domains (32T25) Analytic subsets and submanifolds (32C25) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (1)

Interpolation in weakly pseudoconvex domains in \({\mathbb{C}}^ 2\)

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