Paley–Wiener Functions with a Generalized Spectral Gap
✍ Scribed by N. Blank; A. Ulanovskii
- Publisher
- SP Birkhäuser Verlag Boston
- Year
- 2010
- Tongue
- English
- Weight
- 427 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1069-5869
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📜 SIMILAR VOLUMES
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
In this paper we establish a Paley᎐Wiener theorem for the Hankel transformation on generalized functions of Colombeau type.
On a symmetric space X=GÂK of noncompact type, we consider the formulas where 8 \* is the spherical function on X. Taken together they represent, the synthesis and decomposition formulas for appropriate functions f on X in terms of joint eigenfunctions of the invariant differential operators on X.