## Abstract In this paper we define the __K__~ΞΌ~β transformation on certain spaces of generalized functions introduced by A.C. McBride by employing the kernel method. we also establish relations between the generalized __K__~ΞΌ~β transformation and certain fractional integral operators.
The Laplace Transformation on Certain Spaces of Generalized Functions
β Scribed by A. Baier; H.-J. Glaeske
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 409 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0025-584X
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π SIMILAR VOLUMES
In this paper the generalized fractional integration operators defined by KIRYAKOVA [6], [7] are expressed in terms of the Laplace transform L and its inverse L -' . These decomposition results are established on L, spaces and some examples are deduced as their special cases.
Necessary and sufficient conditions are given for a Banach-space-valued function f to be the Laplace-Stieltjes transform of a function of bounded variation. These conditions are used to obtain generation theorems for both absolutely continuous integrated semigroups and Abel summable semigroups.