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

Title:

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

Creator:

Damyanov, Blagovest P.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:fabbdff8-3658-4039-a7a5-bea587c81edf
uuid:fabbdff8-3658-4039-a7a5-bea587c81edf

Subject:

Schwartz distributions, multiplication, and Colombeau generalized functions

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

189-201

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:1

Harvested from:

CDK

Metadata only:

false