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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Revista matemática complutense Jg. 31; H. 3; S. 651 - 672
Hauptverfasser: Aron, Richard M., Falcó, Javier, García, Domingo, Maestre, Manuel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Milan Springer Milan 01.09.2018
Springer Nature B.V
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-018-0261-x