Non-standard version of Egorov algebra of generalized functions

DOI10.1007/978-3-031-48579-4_21zbMath1548.46035MaRDI QIDQ6547681

Todor D. Todorov

Publication date: 30 May 2024

zbMATH Keywords

Colombeau algebrapartial differential equationsSchwartz distributionsgeneralized functionstransfer principleinfinitesimalsnon-standard analysismultiplication of distributionssaturation principlenon-standard real numbersEgorov algebranon-standard complex numberssheaf of differential functional spacesunderflow principle

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) PDEs with low regular coefficients and/or low regular data (35R05) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Models with special properties (saturated, rigid, etc.) (03C50) Nonstandard models in mathematics (03H05) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Nonstandard functional analysis (46S20) Presheaves and sheaves in general topology (54B40)

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