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

Abstract

Abstract 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