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p ‐Adic Colombeau‐Egorov type theory of generalized functions
Author(s) -
Albeverio S.,
Khrennikov A. Yu.,
Shelkovich V. M.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310222
Subject(s) - mathematics , generalized function , convolution (computer science) , fourier transform , multiplication (music) , pure mathematics , operator (biology) , type (biology) , mathematical analysis , algebra over a field , combinatorics , artificial intelligence , repressor , biology , artificial neural network , computer science , transcription factor , ecology , biochemistry , chemistry , gene
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)