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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 657-672

Wavelet transforms in generalized Fock spaces

1Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, Virginia 23284-201, USA
2Institute of Mathematics, University of Novi Sad, TRG D. OBRADOVIĆA 4, Novi Sad 21000 , Serbia

Received 26 March 1996; Revised 27 May 1996

Copyright © 1997 Hindawi Publishing Corporation. 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.


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.