Uncertainty principles associated to non-degenerate quadratic forms
Mémoires de la Société Mathématique de France, no. 119 (2009), 96 p.
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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.

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.

DOI : https://doi.org/10.24033/msmf.431
Classification:  30H99,  32A15,  42B10
Keywords: Fourier Transforms, uncertainty principles, Lorentz cone, Bargmann transform, Fock space, Cayley transform, tempered distribution
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     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},
     zbl = {1211.42010},
     mrnumber = {2760896},
     language = {en},
     url = {http://www.numdam.org/item/MSMF_2009_2_119__1_0}
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Demange, Bruno. Uncertainty principles associated to non-degenerate quadratic forms. Mémoires de la Société Mathématique de France, Serie 2, , no. 119 (2009), 96 p. doi : 10.24033/msmf.431. http://www.numdam.org/item/MSMF_2009_2_119__1_0/

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