Balanced Colombeau products of the distributions $x_{\pm}^{-p}$ and $x^{-p}$

B. P. Damyanov

Balanced Colombeau products of the distributions $x_{\pm}^{-p}$ and $x^{-p}$

Functional Analysis 2007-05-23 v1

Authors: B. P. Damyanov

Abstract

Results on singular products of the distributions $x_{\pm}^{-p}$ and $x^{-p}$ for natural $p$ are derived when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusi\'nski in 1966. The results are obtained in Colombeau algebra of generalized functions, which is most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.

Keywords

Colombeau algebra distributions singular products balanced products generalized functions Schwartz distributions

Cite

@article{arxiv.math/0203251,
  title  = {Balanced Colombeau products of the distributions $x_{\pm}^{-p}$ and $x^{-p}$},
  author = {B. P. Damyanov},
  journal= {arXiv preprint arXiv:math/0203251},
  year   = {2007}
}

Comments

11 pages

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