9 citations · 24 across the 19 of their papers we have counts for
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Algebraic Approach to Colombeau Theory
Todor D. Todorov
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…
An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms
Todor D. Todorov
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sen…
Lecture Notes: Non-Standard Approach to J.F. Colombeau's Theory of Generalized Function: University of Vienna, Austria, May 2006
Todor D. Todorov
In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physicists and engineers who do research on J. F.…
An axiomatic approach to non-linear theory of generalized functions
Todor D. Todorov
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 t…
Full Algebra of Generalized Functions and Non-Standard Asymptotic Analysis
Todor D. Todorov, Hans Vernaeve
We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of…
Pointwise Values and Fundamental Theorem in the Algebra of Asymptotic Functions
Todor D. Todorov
We show that the algebra of asymptotic functions (introduced in another paper by the author of this article jointly with M. Oberguggenberger) is isomorphic to a…