Hankel Transformation of Colombeau Type Tempered Generalized Functions
✍ Scribed by Jorge J Betancor; Lourdes Rodrı́guez-Mesa
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 309 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
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.
📜 SIMILAR VOLUMES
In this paper we establish a Paley᎐Wiener theorem for the Hankel transformation on generalized functions of Colombeau type.
## Abstract The __p__‐adic Colombeau‐Egorov algebra of generalized functions on ℚ__^n^~p~__ is constructed. For generalized functions the operations of multiplication, Fourier‐transform, convolution, taking pointvalues are defined. The operations of (fractional) partial differentiation and (fractio
## Abstract Generalized functions as mappings defined on the set of generalized points are considered. Local properties of generalized functions, singular support and various types of 𝒢^∞^–regularity are analyzed. Suppleness and non–flabbyness are proved. Necessary and sufficient conditions on gene
We define the Laplace transformation for elements of Colombeau's spaces \(\mathscr{\varphi}_{c}\left(\mathbf{R}^{n}\right), \mathscr{G}_{c}^{x}\left(\mathbf{R}^{n}\right)\) and \(\mathscr{G}_{1}(\Gamma)\), where \(\Gamma\) is a cone. We obtain, in Theorems 1,2 , and 4 , the "expected" Paley-Wiener t