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A classification of homogeneous operators in the Cowen-Douglas class

Koranyi, Adam and Misra, Gadadhar (2011) A classification of homogeneous operators in the Cowen-Douglas class. In: Advances in Mathematics, 226 (6). pp. 5338-5360.

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Official URL: http://dx.doi.org/10.1016/j.aim.2011.01.012

Abstract

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc D is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous holomorphic Hermitian vector bundles over D, the ones corresponding to operators in the Cowen-Douglas class B-n(D) are identified. The classification of homogeneous operators in B-n(D) is completed using an explicit realization of these operators. We also show how the homogeneous operators in B-n(D) split into similarity classes. (C) 2011 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Elsevier science.
Keywords: Hermitizable;Cowen-Douglas class;Reproducing kernel; Homogeneous holomorphic Hermitian vector bundles.
Department/Centre: Others
Date Deposited: 06 Apr 2011 12:59
Last Modified: 06 Apr 2011 12:59
URI: http://eprints.iisc.ernet.in/id/eprint/36386

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