A new Approach to Temperate Generalized Colombeau Functions
Publications de l'Institut Mathématique, _N_S_84 (2008) no. 98, p. 109
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
A new approach to the algebra $\Cal G_\tau$
of temperate nonlinear generalized functions is proposed,
in which $\Cal G_\tau$ is based on the space $\Cal O_M$
endowed with is natural topology in contrary to previous constructions.
Thus, this construction fits perfectly in the general scheme
of construction of Colombeau type algebras
and reveals better properties of $\Cal G_\tau$.
This is illustrated by the natural introduction
of a regularity theory in $\Cal G_\tau$,
of the Fourier transform, with the definition of $\Cal G_{\Cal O'_C}$,
the space of rapidly generalized distributions
which is the Fourier image of $\Cal G_\tau$.
@article{10_2298_PIM0898109D,
author = {Antoine Delcroix},
title = {A new {Approach} to {Temperate} {Generalized} {Colombeau} {Functions}},
journal = {Publications de l'Institut Math\'ematique},
pages = {109 },
publisher = {mathdoc},
volume = {_N_S_84},
number = {98},
year = {2008},
doi = {10.2298/PIM0898109D},
zbl = {1274.46081},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0898109D/}
}
TY - JOUR AU - Antoine Delcroix TI - A new Approach to Temperate Generalized Colombeau Functions JO - Publications de l'Institut Mathématique PY - 2008 SP - 109 VL - _N_S_84 IS - 98 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2298/PIM0898109D/ DO - 10.2298/PIM0898109D LA - en ID - 10_2298_PIM0898109D ER -
Antoine Delcroix. A new Approach to Temperate Generalized Colombeau Functions. Publications de l'Institut Mathématique, _N_S_84 (2008) no. 98, p. 109 . doi: 10.2298/PIM0898109D
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