REPRODUCING KERNEL FOR A CLASS OF WEIGHTED BERGMAN SPACES ON THE SYMMETRIZED POLYDISC

Misra, Gadadhar and Roy, Subrata Shyam and Zhang, Genkai (2013) REPRODUCING KERNEL FOR A CLASS OF WEIGHTED BERGMAN SPACES ON THE SYMMETRIZED POLYDISC. In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 141 (7). pp. 2361-2370.

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Abstract

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.

Item Type:	Journal Article
Publication:	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Publisher:	AMER MATHEMATICAL SOC
Additional Information:	copyright for this article belongs to AMER MATHEMATICAL SOC,USA
Keywords:	Symmetrized polydisc; permutation group; sign representation; Schur functions; weighted Bergman space; Hardy space; weighted Bergman kernel; Szego kernel
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Dec 2013 12:21
Last Modified:	30 Dec 2013 12:21
URI:	http://eprints.iisc.ac.in/id/eprint/47991

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