Title

Existence and uniqueness of v-asymptotic expansions and Colombeau’s generalized numbers

Author Info

Todor D. Todorov, California Polytechnic State University - San Luis ObispoFollow

Recommended Citation

Postprint version. Published in Journal of Mathematical Analysis and Applications, Volume 312, Issue 1, December 1, 2005, pages 261-279.

The definitive version is available at https://doi.org/10.1016/j.jmaa.2005.03.042.

Abstract

We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of the v-asymptotic expansion of an integral with a large parameter. As another application (with significance in the non-linear theory of generalized functions) we show that every Colombeau’s generalized number has a v-asymptotic expansion. A similar result follows for Colombeau’s generalized functions, in particular, for all Schwartz distributions.

Disciplines

Mathematics

Copyright

2005 Elsevier.