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Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc

G. Misra ; S. S. Roy ; Genkai Zhang (Institutionen för matematiska vetenskaper, matematik)
Proceedings of the American Mathematical Society (0002-9939). Vol. 141 (2013), 7, p. 2361-2370.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Symmetrized polydisc, permutation group, sign representation, Schur functions, weighted Bergman, PROPER HOLOMORPHIC MAPPINGS, GEOMETRY


Article Number: PII S 0002-9939(2013)11514-5



Denna post skapades 2013-12-13. Senast ändrad 2016-07-12.
CPL Pubid: 189163

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur