Ensembles pics pour \(A^\infty(D)\)

DOI10.5802/aif.757zbMath0398.32004OpenAlexW2334389704MaRDI QIDQ1254435

Jacques Chaumat, Anne-Marie Chollet

Publication date: 1979

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1979__29_3_171_0

zbMATH Keywords

boundary behaviourstrongly pseudoconvex domainpeak pointpicalgebras of holomorphic function

Mathematics Subject Classification ID

Topological linear spaces of continuous, differentiable or analytic functions (46E10) Boundary behavior of holomorphic functions of several complex variables (32A40) Picard-type theorems and generalizations for several complex variables (32H25) Algebras of holomorphic functions of several complex variables (32A38) Pseudoconvex domains (32T99)

Related Items (18)

Ensembles de zéros et d'interpolation à la frontière de domaines strictement pseudoconvexes. (Zero sets and interpolation on the boundary of strictly pseudoconvex domains) ⋮ On dense ideals in spaces of analytic functions ⋮ On the extension of CR-functions ⋮ Maximum modulus sets ⋮ Proper holomorphic maps between balls in one co-dimension ⋮ A peak set of Hausdorff dimension \(2n-1\) for the algebra \(A(D)\) in the boundary of a domain \(D\) with \(C^\infty\)-boundary in \(\mathbb C^n\). ⋮ Characterization of global peak sets for \(A^\infty\)(D) ⋮ Maximum modulus sets in pseudoconvex boundaries ⋮ Applications holomorphes propres continues de domaines strictement pseudoconvexes de \({\mathbb{C}}^ n\) dans la boule unité de \({\mathbb{C}}^{n+1}\). (On the extension of proper holomorphic mappings from strictly pseudoconvex domains in \({\mathbb{C}}^ n\) into the unit ball of \({\mathbb{C}}^{n+1})\) ⋮ Unnamed Item ⋮ Maximum modulus sets and reflection sets ⋮ Closed finitely generated ideals in algebras of holomorphic functions and smooth to the boundary in strictly pseudoconvex domains ⋮ Peak sets in weakly pseudoconvex domains ⋮ Properties of peak sets in weakly pseudoconvex boundaries in \({\mathbb{C}}^ 2\) ⋮ Non division dans \(A^{\infty}(\Omega)\) ⋮ Ensembles pics pour \(A^{\infty}(D)\) non globalement inclus dans une variété integrale ⋮ Interpolation by holomorphic functions smooth to the boundary in the unit ball of \({\mathbb{C}}^ n\) ⋮ Non division dans \(A^{\infty}(\Omega)\). (No factorization in \(A^{\infty}(\Omega))\)

Cites Work

• Extending functions from submanifolds of the boundary
• Smooth zero sets and interpolation sets for some algebras of holomorphic functions on strictly pseudoconvex domains
• Peak-interpolation sets of class \(C^1\)
• Ensembles pics dans des domaines strictement pseudo-convexes
• Holomorphic approximation and hyperfunction theory on a C\(^1\) totally real submanifold of a complex manifold
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Global Regularity for $\overline \partial$ on Weakly Pseudo-Convex Manifolds
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
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