The aim of this paper is to derive by elementary means a theorem on the representation of certain distributions in the form of a Fourier integral. The approach chosen was found suitable especially for students of post-graduate courses at technical universities, where it is in some situations necessary to restrict a little the extent of the mathematical theory when concentrating on a technical problem.
For each () it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to . There is an exchange theorem and inversion in norm.
In this paper the index transformation
A kernel theorem for spaces of Laplace ultradistributions supported by an n-dimensional cone of product type is stated and proved.
In the literature a Boehmian space containing all right-sided Laplace transformable distributions is defined and studied. Besides obtaining basic properties of this Laplace transform, an inversion formula is also obtained. In this paper we shall improve upon two theorems one of which relates to the continuity of this Laplace transform and the other is concerned with the inversion formula.
In this note we show that the two definitions of generalized index -transform given in the previous works [1] and [2] agree for distributions of compact support.