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A new approach to temperate generalized functions

Abstract : A new approach to the algebra G_{τ} of temperate nonlinear generalized functions is proposed, in which G_{τ} is based on the space 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 G_{τ}. This is illustrated by the natural introduction of a regularity theory in G_{τ}, of the Fourier transform, with the definition of G_{O_{C}′}, the space of rapidly generalized distributions which is the Fourier image of G_{τ}.
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https://hal.archives-ouvertes.fr/hal-00201458
Contributor : Antoine Delcroix Connect in order to contact the contributor
Submitted on : Saturday, December 29, 2007 - 4:33:18 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:28 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 3:50:13 PM

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  • HAL Id : hal-00201458, version 1
  • ARXIV : 0801.0074

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Antoine Delcroix. A new approach to temperate generalized functions. Publ. Inst.Math. (Beograd) (N.S.), 2008, 84 (98), pp.109-121. ⟨hal-00201458⟩

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