Fonctions généralisées et analyse non standard |
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Authors: | Antoine Delcroix |
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Institution: | (1) IUFM des Antilles et de la Guyane, Morne Ferret, BP 399, 97159 Pointe-à-Pitre Cedex (Guadeloupe, F. W. I.);(2) Département de Mathématiques et d'Informatique, Université des Antilles et de la Guyane, Campus de Fouillole, BP 592, 97159 Pointe-à-Pitre Cedex (Guadeloupe, F. W. I.) |
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Abstract: | We study some connections between Non-Standard Analysis and algebraical theories of generalized functions. More precisely, we point out the fact that the construction of these algebras can be interpreted in terms of Non Standard asymptotic properties. For example, we show that the construction of the J. F. Colombeau'Algebra is equivalent (in a certain sense) to a monadic property. Conversely, we show that a certain galactic property (being exponentially small with respect to a parameter) leads to a new algebra. |
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Keywords: | 34E15 03H05 03C62 26E35 28E05 30G06 34C35 46F99 |
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