Algebras of symmetric holomorphic functions of several complex variables

Given a proper holomorphic mapping g : Ω ⊆ C n ⟶ Ω ′ ⊆ C n and an algebra of holomorphic functions B (e.g. P ( K ) where K ⊂ Ω is a compact set, H ( U ) , A ( U ) or H ∞ ( U ) where U is an open and bounded set with U ¯ ⊂ Ω ), we study the subalgebra B g of all functions compatible with the equivale...

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Bibliographic Details
Published in:Revista matemática complutense Vol. 31; no. 3; pp. 651 - 672
Main Authors: Aron, Richard M., Falcó, Javier, García, Domingo, Maestre, Manuel
Format: Journal Article
Language:English
Published: Milan Springer Milan 01.09.2018
Springer Nature B.V
Subjects:
Algebra
Analysis
Analytic functions
Applications of Mathematics
Complex variables
Geometry
H infinity
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Permutations
Topology
Secondary 30H05
Several complex variables
05E05
Symmetric holomorphic functions
Algebras of holomorphic functions
Symmetrized polydisk
Primary 32A38
Fibers
ISSN:1139-1138, 1988-2807
Online Access:Get full text
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Summary:Given a proper holomorphic mapping g : Ω ⊆ C n ⟶ Ω ′ ⊆ C n and an algebra of holomorphic functions B (e.g. P ( K ) where K ⊂ Ω is a compact set, H ( U ) , A ( U ) or H ∞ ( U ) where U is an open and bounded set with U ¯ ⊂ Ω ), we study the subalgebra B g of all functions compatible with the equivalence relation defined by the proper mapping g . We provide alternative representations of these algebras and describe the fibers in their spectra. Among other examples we relate the algebras of functions that are invariant under permutations and the algebras of functions defined on the symmetrized polydisk.
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ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-018-0261-x