A study on a class of modified Bessel-type integrals in a Fréchet space of Boehmians

Abstract

In this paper, an attempt is being made to discuss a class of modified Bessel- type integrals on a set of generalized functions known as Boehmians. We show that the modified Bessel-type integral, with appropriately defined convolution products, obeys a fundamental convolution theorem which consequently justifis pursuing analysis in the Boehmian spaces. We describe two Fréchet spaces of Boehmians and extend the modifid Bessel-type integral between the diferent spaces. Furthermore, a convolution theorem and a class of basic properties of the extended integral such as linearity, continuity and compatibility with the classical integral, which provide a convenient extention to the classical results, have been derived