Little Hankel operators on the half plane |
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Authors: | Namita Das Jonathan R. Partington |
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Affiliation: | (1) Department of Pure Mathematics, University of Leeds, LS2 9JT Leeds, England |
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Abstract: | In this paper we consider a class of weighted integral operators onL2 (0, ) and show that they are unitarily equivalent to Hankel operators on weighted Bergman spaces of the right half plane. We discuss conditions for the Hankel integral operator to be finite rank, Hilbert-Schmidt, nuclear and compact, expressed in terms of the kernel of the integral operator. For a particular class of weights these operators are shown to be unitarily equivalent to little Hankel operators on weighted Bergman spaces of the disc, and the symbol correspondence is given. Finally the special case of the unweighted Bergman space is considered and for this case, motivated by approximation problems in systems theory, some asymptotic results on the singular values of Hankel integral operators are provided. |
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Keywords: | 47B35 47B06 47B38 |
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