2010/07/13 by Тодор Д. Тодоров, Todorov, Todor D.
Arts and Humanities · Mathematics · Medicine · #12J15 #12J25 #16W60 #46F10 #Clinical Reasoning and Diagnostic Skills #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #Philosophy and History of Science #Primary 46F30. Secondary: 46S10
paper · pdf · doi:10.48550/arxiv.1007.2223
openalex publication_date 2010/07/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of \em Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. The article is aimed at mathematicians and physicists who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.