THE BERGMAN KERNEL FUNCTION

Misra, Gadadhar (2010) THE BERGMAN KERNEL FUNCTION. In: Indian Journal of Pure and Applied Mathematics, 41 (1, Sp.). pp. 189-197.

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Abstract

In this note, we point out that a large family of n x n matrix valued kernel functions defined on the unit disc D subset of C, which were constructed recently in [9], behave like the familiar Bergman kernel function on ID in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered using this likeness.

Item Type:	Journal Article
Publication:	Indian Journal of Pure and Applied Mathematics
Publisher:	Indian National Science Academy.
Additional Information:	Copyright of this article belongs to Indian National Science Academy.
Keywords:	Berezin-Wallach set; the bi-holomorphic automorphism group; discrete series representation; kernel function; multiplication operator; homogeneous operator; subnormal operator
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 Mar 2010 09:47
Last Modified:	19 Sep 2010 05:58
URI:	http://eprints.iisc.ac.in/id/eprint/26654

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