A Quadratic-Phase Integral Operator for Sets of Generalized Integrable Functions

Abstract

In this paper, we aim to discuss the classical theory of the quadratic-phase integral operator on sets of integrable Boehmians. We provide delta sequences and derive convolution theorems by using certain convolution products of weight functions of exponential type. Meanwhile, we make a free use of the delta sequences and the convolution theorem to derive the prerequisite axioms, which essentially establish the Boehmian spaces of the generalized quadratic-phase integral operator. Further, we nominate two continuous embeddings between the integrable set of functions and the integrable set of Boehmians. Furthermore, we introduce the definition and the properties of the generalized quadratic-phase integral operator and obtain an inversion formula in the class of Boehmians.