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Hankel Operators on Segal-Bargmann Spaces

In: Proceedings of the International Conference on Stochastic Analysis and Applications

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  • Thomas Deck

    (Universität Mannheim, Fakultät für Mathematik und Informatik)

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.

Suggested Citation

  • Thomas Deck, 2004. "Hankel Operators on Segal-Bargmann Spaces," Springer Books, in: Sergio Albeverio & Anne Boutet de Monvel & Habib Ouerdiane (ed.), Proceedings of the International Conference on Stochastic Analysis and Applications, pages 17-36, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-2468-9_2
    DOI: 10.1007/978-1-4020-2468-9_2
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