Convolutions and applications for the offset linear canonical transform via Hermite weights

The main purpose of this paper is to present three new convolutions for the offset linear canonical transform, with the Hermite weights, and to illustrated their potential applications. In view of this, new factorization theorems are obtained and new Young’s convolution inequalities will be introduced. Within the more applied side, the way to design filters (including multiplicative filters in the time domain) is also discussed in the last section.