The aim of this paper is to establish an inversion and Calderón formulas for the generalized Gabor transform associated with a class of Sturm–Liouville operators. We also investigate several problems related to reproducing kernel theory for this transform. In particular, we study the concept of Tikhonov regularization and the extremal functions associated with the new generalized Gabor transform.
Ghobber et al. (Fri,) studied this question.