A new Approach to Temperate Generalized Colombeau Functions

Antoine Delcroix

Displaying similar documents to “A new Approach to Temperate Generalized Colombeau Functions”

On the Fourier transform of the symmetric decreasing rearrangements

Philippe Jaming (2011)

Annales de l’institut Fourier

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Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^{2}$ behavior of a Fourier transform of a function over a small set is controlled by the $L^{2}$ behavior of the Fourier transform of its symmetric decreasing rearrangement. In the $L^{1}$ case, the same is true if we further assume that the function has a support of finite measure. As...

Uncertainty principles for the Weinstein transform

Hatem Mejjaoli, Makren Salhi (2011)

Czechoslovak Mathematical Journal

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The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi's theorem, Beurling's theorem, and Donoho-Stark's uncertainty principle are obtained for the Weinstein transform.

On introduction of two diffeomorphism invariant Colombeau algebras

Jiří Jelínek (2004)

Commentationes Mathematicae Universitatis Carolinae

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Equivalent definitions of two diffeomorphism invariant Colombeau algebras introduced in [7] and [5] (Grosser et al.) are listed and some new equivalent definitions are presented. The paper can be treated as tools for proving in [8] the equality of both algebras.