Hankel Operators on Segal-Bargmann Spaces

Thomas Deck
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Thomas Deck: Universität Mannheim, Fakultät für Mathematik und Informatik

A chapter in Proceedings of the International Conference on Stochastic Analysis and Applications, 2004, pp 17-36 from Springer

Abstract: Abstract Hankel operators H b on Segal—Bargmann spaces, with respect to finitely and infinitely many variables, are investigated. A regularity condition on the symbol b which guarantees boundedness of H b is provided, the Hilbert—Schmidtness of H b is characterized, and an integral representation for Hankel operators of Hilbert Schmidt type is given. The proofs partially employ the hypercontractivity of the Ornstein-Uhlenbeck semi-group. The case with infinitely many variables is treated via approximations with finitely many variables.

Keywords: Small Hankel operators; holomorphic Wiener functionals; complex hypercontractivity; Primary; 47B35; 46E20; Secondary; 47D03; 47D07 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-2468-9_2

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DOI: 10.1007/978-1-4020-2468-9_2

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