Funciones no-estándar y teoría de distribuciones
Any sequence of real functions (fn) induces a function f = gen (fn) in the non-standard reals R* by taking the ultraproduct πn and lt; R,fn and gt;/F (F a non-principal ultrafilter). This papeP studies the algebra and the caculus of the functions so obtained. Derivatives and integrals are defined as...
- Autores:
-
Takeuchi, Yu
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1983
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42840
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42840
http://bdigital.unal.edu.co/32937/
- Palabra clave:
- Funciones
teoría de distribuciones
modelo no estándar
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Any sequence of real functions (fn) induces a function f = gen (fn) in the non-standard reals R* by taking the ultraproduct πn and lt; R,fn and gt;/F (F a non-principal ultrafilter). This papeP studies the algebra and the caculus of the functions so obtained. Derivatives and integrals are defined as the obvious non-standard extensions of the corresponding real operators. Continuity instead, is defined via the pseudometric induced by R in R* (f is continuos in ∝ ϵ R* if f(∝ + ε) ≈ f (∝) for infinitesimal ε) . Finally, it is shown that any Schwartz distribution T is represented by a non-standard function f of this kind, in the sense that for any test function g [Formula Matemática]; where g is the canonical extension of g to R*. |
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