New convolutions for the Hartley integral transform imbedded in the Banach algebras and convolution-type integral equations

Abstract

This article presents two types of the new convolutions for the Hartley integral transform associated with the Hermite functions, gives rise to the identification of some commutative and non-commutative Banach algebras, and to the Young inequalities which, in a certain sense, can be seen as the exceptional Young inequalities. Moreover, the solvability of a class of the integral equations is investigated, and their solutions in a series form can be obtained by using the constructed convolutions.

Keywords

• hartley’s integral transform
• generalized convolution
• hermite’s functions
• wiener’s algebra
• 42a38
• 44a20
• 44a35
• 45e10