The classical theory of the Weierstrass transform is extended to a generalized function space which is the dual of a testing function space consisting of purely entire functions with certain growth conditions developed by Kenneth B. Howell. An inversion formula and characterizations for this transfo
Inversion of the Weierstrass transformation for generalized functions
β Scribed by Z Ditzian
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 258 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0022-247X
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In this note the Hankel transformation on a new class of generalized functions of Colombeau type is defined. Also we investigate the Hankel convolution and the Hankel translation on that space of generalized functions.
## 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.