CONVOLUTION OF THE HARTLEY TRANSFORM WITH AN EXTENDED KERNEL AND THE TOEPLITZ PLUS HANKEL INTEGRAL EQUATION

CONVOLUTION OF THE HARTLEY TRANSFORM WITH AN EXTENDED KERNEL AND THE TOEPLITZ PLUS HANKEL INTEGRAL EQUATION

This paper is to propose a new definition of the Hartley transform with an extended kernel which can be considered as a generalized version of the well-known Hartley transform. Moreover, the highlight of the paper is constructing a new convolution associated with the proposed transform, therefore applying it to find the closed-form solutions of a modified type of the Toeplitz plus Hankel integral equation problem. Besides, some basic properties of this transform and proposed convolution such as the Riemann-Lebesgue lemma, inversion theorem, factorization identity, and Young-type inequality will be also derived.