Homogeneous operators on Hilbert spaces of holomorphic functions - I

KorÁnyi, Adam ; Misra, Gadadhar (2008) Homogeneous operators on Hilbert spaces of holomorphic functions - I Journal of Functional Analysis, 254 (9). pp. 2419-2436. ISSN 0022-1236

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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 Mö bius group consisting of bi-holomorphic automorphisms of the unit disc D. For every m ∈ 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 D and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Homogeneous Operators; Homogeneous Holomorphic Hermitian Vector Boundle; Associated Representation; Cowen-Douglas Class; Reproducing Kernel Function
ID Code:66995
Deposited On:28 Oct 2011 10:31
Last Modified:18 May 2016 14:18

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