Towards Oka–Cartan theory for algebras of holomorphic functions on coverings of Stein manifolds I
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Alexander Brudnyi [1] ; Damir Kinzebulatov [2]
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[1] University of Calgary
University of Calgary
Canadá
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[2] Fields Institute for Research in Mathematical Sciences
Fields Institute for Research in Mathematical Sciences
Canadá
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 3, 2015, págs. 989-1032
- Idioma: inglés
- DOI: 10.4171/RMI/861
- Texto completo no disponible (Saber más ...)
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Resumen
We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona-type theorems, properties of divisors, holomorphic analogs of the Peter–Weyl approximation theorem, Hartogs-type theorems, characterization of uniqueness sets. The model examples of these algebras are:
(1) Bohr’s algebra of holomorphic almost periodic functions on tube domains;
(2) algebra of all fibrewise bounded holomorphic functions (e.g., arising in the corona problem for H∞).
Our approach is based on an extension of the classical Oka–Cartan theory to coherent-type sheaves on the maximal ideal spaces of these algebras – topological spaces having some features of complex manifolds.
