The Bergman kernel function

Gadadhar Misra ()
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Gadadhar Misra: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 1, 189-197

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

Keywords: Berezin-Wallach set; the bi-holomorphic automorphism group; discrete series representation; kernel function; multiplication operator; homogeneous operator; subnormal operator (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0010-4

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