A classification of homogeneous operators in the Cowen-Douglas class

Korányia, Adam ; Misra, Gadadhar (2011) A classification of homogeneous operators in the Cowen-Douglas class Advances in Mathematics, 226 (6). pp. 5338-5360. ISSN 0001-8708

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related 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 Bn(D) are identified. The classification of homogeneous operators in Bn(D) is completed using an explicit realization of these operators. We also show how the homogeneous operators in Bn(D) split into similarity classes.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Hermitizable; Cowen-Douglas Class; Reproducing Kernel; Homogeneous Holomorphic Hermitian Vector Bundles
ID Code:88256
Deposited On:27 Mar 2012 13:01
Last Modified:27 Mar 2012 13:01

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