Abstract
The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential and corresponding
-Sobolev space. Moreover, the Schwartz-type space
is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The
-boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces
and
are given.
Acknowledgments
Authors are very thankful to the reviewers for his/her valuable and constructive comments.
Disclosure statement
No potential conflict of interest was reported by the authors.