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