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p-Adic Colombeau-Egorov type theory of generalized functions

✍ Scribed by S. Albeverio; A. Yu. Khrennikov; V. M. Shelkovich

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
206 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 (fractional) partial integration are introduced by the Vladimirov's pseudodifferential operator. The products of Bruhat‐Schwartz distributions are well defined as elements of this algebra. In contrast to the “usual” Colombeau and Egorov ℂ‐theories, where generalized functions on ℝ__^n^__ are not determined by their pointvalues on ℝ__^n^, p‐adic Colombeau‐Egorov generalized functions are uniquely determined by their pointvalues on ℚ^n^~p~__. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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