Algebraic Approach to Colombeau Theory

Autores

  • Todor D. Todorov Mathematics Department, California Polytechnic State University.

DOI:

https://doi.org/10.11606/issn.2316-9028.v7i2p127-142

Palavras-chave:

Totally ordered field, real closed field, algebraically closed field,, non- Archimedean field, infinitesimals, Cantor complete field, saturated field, valuation, field, ultra-metric, Hahn-Banach theorem,, monad, function, Schwartz distributions, Colombeau algebra, Colombeau embedding

Resumo

We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions, and the set of regular distributions with C ∞-kernels forms a differential subalgebra. We discuss the uniqueness of the field of scalars as well as the consistency and independence of our axioms. This article is written mostly to satisfy the interest of mathematicians and scientists who do not necessarily belong to the Colombeau community; that is to say, those who do not necessarily work in the non-linear theory of generalized functions.

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Biografia do Autor

  • Todor D. Todorov, Mathematics Department, California Polytechnic State University.
    Mathematics Department, California Polytechnic State University, San Luis Obispo, California 93407, USA

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Edição

v. 7 n. 2 (2013)

Seção

Artigos

Como Citar

Algebraic Approach to Colombeau Theory. (2013). São Paulo Journal of Mathematical Sciences, 7(2), 127-142. https://doi.org/10.11606/issn.2316-9028.v7i2p127-142