Results on generalized models and singular products of distributions in the Colombeau algebra
Commentationes Mathematicae Universitatis Carolinae (2015)
- Volume: 56, Issue: 2, page 145-157
- ISSN: 0010-2628
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topDamyanov, Blagovest. "Results on generalized models and singular products of distributions in the Colombeau algebra $\mathcal {G}(\mathbb {R})$." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 145-157. <http://eudml.org/doc/270110>.
@article{Damyanov2015,
abstract = {Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea of a well-known result of Jan Mikusiński on balancing of singular distributional products.},
author = {Damyanov, Blagovest},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Colombeau algebra; singular products of distributions; Colombeau algebra; singular products of distributions},
language = {eng},
number = {2},
pages = {145-157},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Results on generalized models and singular products of distributions in the Colombeau algebra $\mathcal \{G\}(\mathbb \{R\})$},
url = {http://eudml.org/doc/270110},
volume = {56},
year = {2015},
}
TY - JOUR
AU - Damyanov, Blagovest
TI - Results on generalized models and singular products of distributions in the Colombeau algebra $\mathcal {G}(\mathbb {R})$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 145
EP - 157
AB - Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea of a well-known result of Jan Mikusiński on balancing of singular distributional products.
LA - eng
KW - Colombeau algebra; singular products of distributions; Colombeau algebra; singular products of distributions
UR - http://eudml.org/doc/270110
ER -
References
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- Mikusiński J., On the square of the Dirac delta-distribution, Bull. Acad. Pol. Ser. Sci. Math. Astron. Phys. 43 (1966), 511–513. Zbl0163.36404MR0203392
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- Oberguggenberger M., Multiplication of Distributions and Applications to PDEs, Longman, Essex, 1992.
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