Compact Hankel Forms on Planar Domains |
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Authors: | Vasiliy A Prokhorov Mihai Putinar |
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Institution: | (1) Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688-0002, USA;(2) Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080, USA |
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Abstract: | A Hankel form on a Hilbert function space is a bounded, symmetric, bilinear form ., .] satisfying fx, y] = x, fy] for a class of multipliers f. We prove analogs of Weyl–Horn and Ky Fan inequalities for compact Hankel forms, and apply them to estimate the related eigenvalues,
both for Hardy–Smirnov and Bergman spaces norms associated to multiply connected planar domains. In the case of the unit disk,
we investigate the asymptotic of some measures constructed by eigenfunctions of Hankel operators with certain Markov functions
as symbols.
Submitted: May 2, 2008. Accepted: June 28, 2008. |
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Keywords: | " target="_blank"> Bilinear symmetric form singular number meromorphic approximation rational approximation |
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