arXiv subjects

B. P. Damyanov

Publications and source records attributed to B. P. Damyanov.

2 recordsLinked to original sources

arXiv2002

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

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 Mikusiński 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.

math.FA↗

arXiv2002

On balanced products of the distributions $x_{\pm}^{a}$ in Colombeau algebra $\EuScript{G}(\mathbb{R})$

Results on products of the distributions $x_{\pm}^{a}$ and $\de^{(p)}(x)$ with coinciding singularities are derived when the products are balanced so that they exist in the distribution space. These results follow the idea of a known result on distributional products published by Jan Mikusiński in 1966. They are obtained in Colombeau algebra $\EuScript{G}(\mathbb{R})$ of generalized functions that contains the distribution space and the notion of 'association' in it allows obtaining results in terms of distributions.

math.FA↗