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Non-compactness of the solution operator to on the Fock-space in several dimensions

✍ Scribed by Georg Schneider

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 121 KB
Volume: 278
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310242

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✦ Synopsis

Abstract

We consider the canonical solution operator to $ \bar \partial $ restricted to (0, 1)‐forms with coefficients in the generalized Fock‐spaces

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We will show that the canonical solution operator restricted to (0, 1)‐forms with $ {\cal F}{m} $‐coefficients can be interpreted as a Hankel‐operator. Furthermore we will show that the canonical solution operator is not compact for m ≥ 2. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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