Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc
Journal article, 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.
PROPER HOLOMORPHIC MAPPINGS
Schur functions
weighted Bergman
permutation group
GEOMETRY
sign representation
Symmetrized polydisc
Author
G. Misra
Indian Institute of Science
S. S. Roy
Indian Institute of Science
Genkai Zhang
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Proceedings of the American Mathematical Society
0002-9939 (ISSN) 1088-6826 (eISSN)
Vol. 141 7 2361-2370Subject Categories
Mathematics
DOI
10.1090/S0002-9939-2013-11514-5