# Homogeneous operators on Hilbert spaces of holomorphic functions-I

Korányi, Adam and Misra, Gadadhar (2008) Homogeneous operators on Hilbert spaces of holomorphic functions-I. In: Journal of Functional Analysis, 254 (9). pp. 2419-2436.

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## Abstract

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are homogeneous with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit disc $\mathbb D$. For every $m \in N$ we have a family of operators depending on m+1 positive real parameters. The kernel function is calculated explicitly. It is proved that each of these operators is bounded, lies in the Cowen-Douglas class of $\mathbb D$ and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent.

Item Type: Journal Article Copyright of this article belongs to Elevier. Homogeneous operators;Homogeneous holomorphic Hermitian vector boundle;Associated representation;Cowen–Douglas class;Reproducing kernel function Division of Physical & Mathematical Sciences > Mathematics 27 Jun 2008 19 Sep 2010 04:46 http://eprints.iisc.ernet.in/id/eprint/14556