Convolution for a pair of quadratic-phase Hankel transforms

Abstract

In this work, a pair of quadratic-phase Hankel (QPH) transforms is introduced and defined their inversion. Moreover, some differential operators are given, and two variants of Bessel differential operators are defined. Further two different types of Zemanian spaces are defined and discussed the continuity of QPH-transform and given differential operators on these spaces. Next, we extend the QPHT to generalized functions. QPH-translation and convolution are also defined and studied their properties. Furthermore, an application of QPH-transform to a generalized non-linear parabolic equation is given.