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.
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