Wave packet transform and fractional wave packet transform of rapidly decreasing functions

Abstract

The continuity of wave packet transform and inverse wave packet transform is proved in the suitable Schwartz space and extended to its corresponding dual space of tempered distribution. The consistency, linearity and continuity of the transform with respect to [Formula: see text] topology are proved in this distribution space. Further, the continuity of the fractional wave packet transform and its inverse in the above space is proved. The examples of generalized fractional wave packet transform of certain distributions are given.