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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 530473, 12 pages
http://dx.doi.org/10.5402/2012/530473
Research Article

Resolution of the Identity of the Classical Hardy Space by Means of Barut-Girardello Coherent States

Department of Mathematics, Faculty of Sciences and Technics (M'Ghila), Sultan Moulay Slimane University, BP 523, Beni Mellal, Morocco

Received 11 April 2012; Accepted 31 May 2012

Academic Editors: V. Moretti and W.-H. Steeb

Copyright © 2012 Zouhaïr Mouayn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We construct a one-parameter family of coherent states of Barut-Girdrardello type performing a resolution of the identity of the classical Hardy space of complex-valued square integrable functions on the real line, whose Fourier transform is supported by the positive real semiaxis.