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.
We generalize to the case of several variables the classical theorems on the holomorphic extension of the Cauchy transforms. The Cauchy transformation is considered in the setting of tempered distributions and the Cauchy kernel is modified to a rapidly decreasing function. The results are applied to the study of "continuous" Taylor expansions and to singular partial differential equations.
An integral transform denoted by that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.