Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc
Artikel i vetenskaplig tidskrift, 2013
A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to compute the kernel function for the weighted Bergman spaces on the symmetrized polydisc using the explicit nature of our embedding. This family of kernel functions includes the Szego and the Bergman kernel on the symmetrized polydisc.
Schur functions
sign representation
Symmetrized polydisc
weighted Bergman
permutation group
GEOMETRY
PROPER HOLOMORPHIC MAPPINGS
Författare
G. Misra
Indian Institute of Science
S. S. Roy
Indian Institute of Science
Genkai Zhang
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Matematik
Proceedings of the American Mathematical Society
0002-9939 (ISSN) 1088-6826 (eISSN)
Vol. 141 7 2361-2370Ämneskategorier
Matematik
DOI
10.1090/S0002-9939-2013-11514-5