## 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
Group invariant Colombeau generalized functions
✍ Scribed by Hans Vernaeve
- Book ID
- 106198516
- Publisher
- Springer Vienna
- Year
- 2007
- Tongue
- English
- Weight
- 119 KB
- Volume
- 153
- Category
- Article
- ISSN
- 0026-9255
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📜 SIMILAR VOLUMES
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.
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
## 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