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A Paley–Wiener theorem for Bergman spaces with application to invariant subspaces

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Duren, Peter and Gallardo Gutiérrez, Eva A. and Montes Rodríguez, Alfonso (2007) A Paley–Wiener theorem for Bergman spaces with application to invariant subspaces. Bulletin of the London Mathematical Society, 39 (3). pp. 459-466. ISSN 1469-2120

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Abstract

An analogue of the Paley-Wiener theorem is developed for weighted Bergman spaces of analytic functions in the upper half-plane. The result is applied to show that the invariant subspaces of the shift operator on the standard Bergman space of the unit disk can be identified with those of a convolution Volterra operator on the space L 2 (ℝ + ,(1/t)dt).


Item Type:Article
Uncontrolled Keywords:MSC 2010 30H05 Bounded analytic functions; Hilbert spaces of continuous, differentiable or analytic functions; Invariant subspaces of linear operators
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21070
Deposited On:25 Apr 2013 11:29
Last Modified:05 Sep 2018 16:36

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