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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 1, Pages 13–25 (Mi faa3453)  

Results on the Colombeau Products of the Distribution $x_+^{-r-1/2}$ with the Distributions $x_-^{-k-1/2}$ and $x_-^{k-1/2}$

M. Mitevaa, B. Jolevska-Tuneskab, T. Atanasova-Pacemskaa

a Department of Mathematics, Faculty of Computer Science, University Goce Delcev, Stip, Republic of Macedonia
b Faculty of Electrical Engineering and Informational Technologies, Ss. Cyril and Methodius University, Skopje, Republic of Macedonia

Abstract: Results on the products of the distribution $x_+^{-r-1/2}$ with the distributions $x_-^{-k-1/2}$ and $x_-^{k-1/2}$ are obtained in the differential algebra ${\mathcal{G}}(\mathbb{R})$ of Colombeau generalized functions, which contains the space $\mathcal{D}'(\mathbb{R})$ of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in $\mathcal{G}(\mathbb{R})$. This enables treating the results in terms of distributions again.

Keywords: distribution, Colombeau algebra, Colombeau generalized functions, multiplication of distributions.

DOI: https://doi.org/10.4213/faa3453

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English version:
Functional Analysis and Its Applications, 2018, 52:1, 9–20

Bibliographic databases:

UDC: 517.982.4
Received: 04.11.2016

Citation: M. Miteva, B. Jolevska-Tuneska, T. Atanasova-Pacemska, “Results on the Colombeau Products of the Distribution $x_+^{-r-1/2}$ with the Distributions $x_-^{-k-1/2}$ and $x_-^{k-1/2}$”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 13–25; Funct. Anal. Appl., 52:1 (2018), 9–20

Citation in format AMSBIB
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\paper Results on the Colombeau Products of the Distribution $x_+^{-r-1/2}$ with the Distributions $x_-^{-k-1/2}$ and $x_-^{k-1/2}$
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 1
\pages 13--25
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\crossref{https://doi.org/10.4213/faa3453}
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