International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 4, Pages 657-672
doi:10.1155/S0161171297000914

Wavelet transforms in generalized Fock spaces

John Schmeelk1 and Arpad Takači2

 1Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-201, Virginia, USA
2Institute of Mathematics, University of Novi Sad, TRG D. OBRADOVIĆA 4, Novi Sad 21000 , Serbia
Received 26 March 1996; Revised 27 May 1996

Abstract

A generalized Fock space is introduced as it was developed by Schmeelk [1-5], also Schmeelk and Takači [6-8]. The wavelet transform is then extended to this generalized Fock space. Since each component of a generalized Fock functional is a generalized function, the wavelet transform acts upon the individual entry much the same as was developed by Mikusinski and Mort [9] based upon earlier work of Mikusinski and Taylor [10]. It is then shown that the generalized wavelet transform applied to a member of our generalized Fock space produces a more appropriate functional for certain appfications.