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Hankel operators with antiholomorphic symbols on the Fock space

Author: Georg Schneider
Journal: Proc. Amer. Math. Soc. 132 (2004), 2399-2409
MSC (2000): Primary 47B35; Secondary 32A15
Published electronically: March 24, 2004
MathSciNet review: 2052418
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Abstract: We consider Hankel operators of the form $H_{\overline{z}^k}: \mathcal{F}^m:=\{f : f \mbox{ is entire and} \int_{\mathbb{... ...ert f(z)\vert^2e^{-\vert z\vert^m}<\infty\}\rightarrow L^2(e^{-\vert z\vert^m})$. Here $k,m,n \in \mathbb{N} $. We show that in the case of one complex dimension the Hankel operators are compact but not Hilbert-Schmidt if $m>2k$.

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Additional Information

Georg Schneider
Affiliation: Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
Address at time of publication: Institut für Betriebswirtschaftslehre, Universität Wien, Brünner Strasse 72, A-1210 Wien, Austria

Keywords: Fock space, Hankel operator, reproducing kernel
Received by editor(s): October 25, 2002
Received by editor(s) in revised form: May 15, 2003
Published electronically: March 24, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society

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