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<identifier>oai:HAL:hal-00201458v1</identifier>
<datestamp>2017-12-21</datestamp>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>A new approach to temperate generalized functions</title>
<creator>Delcroix, Antoine</creator>
<contributor>Centre de recherches et de ressources en éducation et formation (CRREF) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>Prelimary version - 13 pages.</description>
<description>International audience</description>
<source>Publ. Inst.Math. (Beograd) (N.S.)</source>
<identifier>hal-00201458</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00201458</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00201458/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00201458/file/NewGOMdec29WithAdditions.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00201458</source>
<source>Publ. Inst.Math. (Beograd) (N.S.), 2008, 84 (98), pp.109-121</source>
<identifier>ARXIV : 0801.0074</identifier>
<relation>info:eu-repo/semantics/altIdentifier/arxiv/0801.0074</relation>
<language>en</language>
<subject lang=en>Rapidly decreasing distributions</subject>
<subject lang=en>Fourier Transform</subject>
<subject lang=en>Temperate distributions</subject>
<subject lang=en>Fourier Transform.</subject>
<subject lang=en>Colombeau generalized functions</subject>
<subject lang=en>Colombeau temperate generalized functions</subject>
<subject lang=en>Rapidly decreasing functions</subject>
<subject lang=en>Schwartz distributions</subject>
<subject>46F30, 46F05, 46E10, 42A38</subject>
<subject>[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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}.</description>
<date>2008</date>
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