Geodesic
A new Approach to Temperate Generalized Colombeau Functions
Publications de l'Institut Mathématique, _N_S_84 (2008) no. 98, p. 109 .

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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 $\Cal G_\tau$.
DOI : 10.2298/PIM0898109D
Classification : 46F30 46F05 46E10 42A38 
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     author = {Antoine Delcroix},
     title = {A new {Approach} to {Temperate} {Generalized} {Colombeau} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {109 },
     publisher = {mathdoc},
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     number = {98},
     year = {2008},
     doi = {10.2298/PIM0898109D},
     zbl = {1274.46081},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0898109D/}
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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. http://geodesic.mathdoc.fr/articles/10.2298/PIM0898109D/

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