Balanced Colombeau products of the distributions and
Czechoslovak Mathematical Journal (2005)
- Volume: 55, Issue: 1, page 189-201
- ISSN: 0011-4642
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topDamyanov, Blagovest. "Balanced Colombeau products of the distributions $x_{\pm }^{-p}$ and $x^{-p}$." Czechoslovak Mathematical Journal 55.1 (2005): 189-201. <http://eudml.org/doc/30937>.
@article{Damyanov2005,
abstract = {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.},
author = {Damyanov, Blagovest},
journal = {Czechoslovak Mathematical Journal},
keywords = {Schwartz distributions; multiplication; Colombeau generalized functions; Schwartz distributions; multiplication; singular products of distributions},
language = {eng},
number = {1},
pages = {189-201},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Balanced Colombeau products of the distributions $x_\{\pm \}^\{-p\}$ and $x^\{-p\}$},
url = {http://eudml.org/doc/30937},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Damyanov, Blagovest
TI - Balanced Colombeau products of the distributions $x_{\pm }^{-p}$ and $x^{-p}$
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 189
EP - 201
AB - 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.
LA - eng
KW - Schwartz distributions; multiplication; Colombeau generalized functions; Schwartz distributions; multiplication; singular products of distributions
UR - http://eudml.org/doc/30937
ER -
References
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