Articles
An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms, Integral Transforms and Special Functions (2011)
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically...
Completeness of the Leibniz Field and Rigorousness of Infinitesimal Calculus (with James F. Hall), ArvixMathematics (2011)
We present a characterization of the completeness of the field of real numbers in the...
Another Proof of the Existence a Dedekind Complete Totally Ordered Field (with James F. Hall), ArvixMathematics (2011)
We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to...
Full algebra of generalized functions and non-standard asymptotic analysis (with Hans Vernaeve), Logic and Analysis (2008)
We construct an algebra of generalized functions endowed with a canonical embedding of the space...
A Lost Theorem: Definite Integrals in An Asymptotic Setting (with Ray Cavalcante), The American Mathematical Monthly (2008)
Conference Proceedings
Pointwise Kernels of Schwartz Distributions, Proceedings of the American Mathematical Society (1992)
We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.
A Nonstandard Delta Function, Proceedings of the American Mathematical Society (1990)
We prove that the Dirac delta distribution has a kernel in the class of the...