[Principes d’incertitude associés à des formes quadratiques non dégénérées]
Ce volume est consacré a des géneralisations du principe d’incertitude classique de Hardy dans les espaces Euclidiens. Au lieu de comparer les fonctions à des gaussiennes, nous les comparons a l’exponentielle de formes quadratiques non dégénérées, par exemple à la forme de Lorentz. Nous transformons ces problèmes à l’aide de la transformée de Bargmann, en des problèmes de description de certaines classes de fonctions entières de plusieurs variables. Ces méthode améliorent et simplifient des résultats publiés dans des travaux précédents.
This volume is devoted to several generalisations of the classical Hardy uncertainty principle on Euclidian spaces. Instead of comparing functions and their Fourier transforms a Gaussian, we compare them to the exponential of general non-degenerate quadratic forms, like for example the Lorentz form. Using the Bargmann transform, we translate the problem into the description of several classes of analytic functions of several variables, and at the same time simplify and unify proofs of results presented in several previous papers.
Keywords: Fourier Transforms, uncertainty principles, Lorentz cone, Bargmann transform, Fock space, Cayley transform, tempered distribution
Mot clés : Transformées de Fourier, principes d’incertitude, cône de Lorentz, transformée de Bargmann, espace de Fock, transformée de Cayley, distribution tempérée
@book{MSMF_2009_2_119__1_0,
author = {Demange, Bruno},
title = {Uncertainty principles associated to non-degenerate quadratic forms},
series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
publisher = {Soci\'et\'e math\'ematique de France},
number = {119},
year = {2009},
doi = {10.24033/msmf.431},
mrnumber = {2760896},
zbl = {1211.42010},
language = {en},
url = {http://www.numdam.org/item/MSMF_2009_2_119__1_0/}
}
TY - BOOK AU - Demange, Bruno TI - Uncertainty principles associated to non-degenerate quadratic forms T3 - Mémoires de la Société Mathématique de France PY - 2009 IS - 119 PB - Société mathématique de France UR - http://www.numdam.org/item/MSMF_2009_2_119__1_0/ DO - 10.24033/msmf.431 LA - en ID - MSMF_2009_2_119__1_0 ER -
Demange, Bruno. Uncertainty principles associated to non-degenerate quadratic forms. Mémoires de la Société Mathématique de France, Série 2, no. 119 (2009), 96 p. doi : 10.24033/msmf.431. http://numdam.org/item/MSMF_2009_2_119__1_0/
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