Pointwise Values and Fundamental Theorem in the Algebra of Asymptotic Functions

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dc.creatorTodorov, Todor D.
dc.date2006-01-30
dc.date.accessioned2026-07-07T06:59:27Z
dc.date.available2026-07-07T06:59:27Z
dc.descriptionWe show that the algebra of asymptotic functions $^ρ\mathcal{E}(Ω)$ (introduced in another paper by the author of this article jointly with M. Oberguggenberger) is isomorphic to a class of pointwise functions in the field of A. Robinson asymptotic numbers $^ρ\mathbb{C}$. Since the algebra $^ρ\mathcal{E}(Ω)$, contains a copy of the Schwartz distributions $\mathcal{D}^\prime(Ω)$, it follows that every Schwartz distribution is a pointwise function in the field $^ρ\mathbb{C}$. The class of asymptotic functions $^ρ\mathcal{E}(Ω)$ is an algebra of generalized functions of Colombeau's type. The field of the constants of this algebra (the functions with zero gradient) coincides with Robinson field $^ρ\mathbb{C}$.The expected applications are to PDE with variable, possibly discontinuous, coefficients and non-linear PDE with singularities.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0601723
dc.identifierhttp://arxiv.org/abs/math/0601723
dc.identifierChapman & Hall/CRC Research Notes in Mathematics, 401, 1999, p. 369-383.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107754
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subject46F30, 03H05,12J25, 46F10, 46S20
dc.titlePointwise Values and Fundamental Theorem in the Algebra of Asymptotic Functions
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