Algebras of symmetric holomorphic functions of several complex variables

作者：Aron Richard M; Falco Javier^*; Garcia Domingo; Maestre Manuel

来源：Revista Matematica Complutense, 2018, 31(3): 651-672.

DOI：10.1007/s13163-018-0261-x

• Symmetric holomorphic functions
• Fibers
• Algebras of holomorphic functions
• Several complex variables
• Symmetrized polydisk

Given a proper holomorphic mapping g : Omega subset of C-n -> Omega' subset of C-n and an algebra of holomorphic functions B (e.g. P(K) where K subset of Omega is a compact set, H(U), A(U) or H-infinity (U) where U is an open and bounded set with (U) over bar subset of Omega), 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.

• 出版日期2018-9