Hilbert-Schmidt Hankel Operators On The Segal-Bargmann Space

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Autoren

  • Wolfram Bauer

Externe Organisationen

  • Johannes Gutenberg-Universität Mainz
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Details

OriginalspracheEnglisch
Seiten (von - bis)2989-2996
Seitenumfang8
FachzeitschriftProceedings of the American Mathematical Society
Jahrgang132
Ausgabenummer10
PublikationsstatusVeröffentlicht - 2 Juni 2004
Extern publiziertJa

Abstract

This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions on ℂn that are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbol g ε L (ℂn) the Hankel operator Hg is of the Hilbert-Schmidt class if and only if H is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operators Hg and H coincide. But, in general, if we deal with bounded symbols, only the inequality ∥H gHS ≤ 2∥HHS can be proved. The results have a close connection with the well-known fact that for bounded symbols the compactness of Hg implies the compactness of H.

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Hilbert-Schmidt Hankel Operators On The Segal-Bargmann Space. / Bauer, Wolfram.
in: Proceedings of the American Mathematical Society, Jahrgang 132, Nr. 10, 02.06.2004, S. 2989-2996.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Bauer W. Hilbert-Schmidt Hankel Operators On The Segal-Bargmann Space. Proceedings of the American Mathematical Society. 2004 Jun 2;132(10):2989-2996. doi: 10.1090/S0002-9939-04-07264-8
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