𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Paley-Wiener Type Theorems for Colombeau′s Generalized Functions

✍ Scribed by M. Nedeljkov; S. Pilipovic

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
460 KB
Volume
195
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

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 type theorems for (\mathscr{G}{c}\left(\mathbf{R}^{n}\right)) and (\mathscr{S}{1}([0, \infty))). The PaleyWiener type theorems are more complicated for elements of (\mathscr{G}{1}(\Gamma)), because the Laplace transformation depends on a cutoff function (Theorem 3). (21995 Academic Press, Inc.

📜 SIMILAR VOLUMES

Paley–Wiener-Type Theorems for a Class o
Paley–Wiener-Type Theorems for a Class of Integral Transforms
✍ Vu Kim Tuan; Ahmed I. Zayed 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 176 KB

A characterization of weighted L 2 I spaces in terms of their images under various integral transformations is derived, where I is an interval (finite or infinite). This characterization is then used to derive Paley-Wiener-type theorems for these spaces. Unlike the classical Paley-Wiener theorem, ou

p-Adic Colombeau-Egorov type theory of g
p-Adic Colombeau-Egorov type theory of generalized functions
✍ S. Albeverio; A. Yu. Khrennikov; V. M. Shelkovich 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 206 KB

## 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