p‐Adic Colombeau‐Egorov type theory of generalized functions

DOI10.1002/mana.200310222zbMath1065.46056OpenAlexW2123807231MaRDI QIDQ4651833

Sergio A. Albeverio, Vladimir Shelkovich, Andrei Yu. Khrennikov

Publication date: 22 February 2005

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200310222

zbMATH Keywords

Fourier transform\(p\)-adic Colombeau--Egorov type algebraproduct of Bruhat--Schwartz distributionsVladimirov's pseudodifferential operator

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Representations of Lie and linear algebraic groups over local fields (22E50) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (4)

Stochastic Processes on Ends of Tree and Dirichlet Forms ⋮ Point value characterizations and related results in the full Colombeau algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^e(\Omega )}$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^d(\Omega )}$\end{document} ⋮ Toward an ultrametric theory of turbulence ⋮ Jump processes on leaves of multibranching trees

Cites Work

• Colombeau generalized functions: A theory based on harmonic regularization
• Anwendungen unendlich kleiner Zahlen. I. Zur Theorie der Distributionen.
• Anwendungen unendlich kleiner Zahlen. II. Ein Zugang zur Operatorenrechnung von Mikusinski.
• Characterization of colombeau generalized functions by their pointvalues
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