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Indian Journal of Pure and Applied Mathematics

, Volume 41, Issue 1, pp 189–197 | Cite as

The Bergman kernel function

  • Gadadhar MisraEmail author
Article

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.

Key words

Berezin-Wallach set the bi-holomorphic automorphism group discrete series representation kernel function multiplication operator homogeneous operator subnormal operator 

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Copyright information

© The Indian National Science Academy 2010

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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