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. Miteva; B. Jolevska-Tuneska; T. Atanasova-Pacemska

Geodesic

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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. Miteva ; B. Jolevska-Tuneska ; T. Atanasova-Pacemska

Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 13-25

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

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.

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

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     author = {M. Miteva and B. Jolevska-Tuneska and T. Atanasova-Pacemska},
     title = {Results on the {Colombeau} {Products} of the {Distribution} $x_+^{-r-1/2}$ with the {Distributions} $x_-^{-k-1/2}$ and $x_-^{k-1/2}$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a1/}
}

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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 $x_-^{k-1/2}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 13-25. http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a1/