Coherent state transforms attached to generalized Bargmann spaces on the complex plane

We construct a family of coherent states transforms attached to generalized Bargmann spaces [C. R. Acad. Sci. Paris, t. 325, 1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the space of square integrable functions on the real line wit...

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Bibliographic Details
Published in:Mathematische Nachrichten 2011-10, Vol.284 (14-15), p.1948-1954
Main Author: Mouayn, Zouhaïr
Format: Article
Language:English
Subjects:
81R30
Bargmann transform
Coherent state transform
generalized Bargmann spaces
MSC 35A22
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Summary:We construct a family of coherent states transforms attached to generalized Bargmann spaces [C. R. Acad. Sci. Paris, t. 325, 1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the space of square integrable functions on the real line with the true‐poly‐Fock spaces [Oper. Theory, Adv. Appl. v. 117, 2000]. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200910191