An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

DOI10.1080/10652469.2010.541057zbMath1238.46037arXiv1101.5740OpenAlexW2125260208MaRDI QIDQ3015107

Todor D. Todorov

Publication date: 8 July 2011

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5740

zbMATH Keywords

Laplace transformColombeau algebraSchwartz distributionsreal closed fieldtotally ordered fieldnon-Archimedean valuation fieldsaturated field

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Laplace transform (44A10) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Ordered fields (12J15)

Related Items

Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations ⋮ The category of Colombeau algebras ⋮ An improved setting for generalized functions: fine ultrafunctions

Cites Work

• On a class of valuation fields introduced by A. Robinson
• An embedding of Schwartz distributions in the algebra of asymptotic functions
• Paley-Wiener type theorems for Colombeau's generalized functions
• Internal sets and internal functions in Colombeau theory
• Allgemeine Bewertungstheorie.
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