Des équations de Dirac et de Schrödinger pour la transformation de Fourier |
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Authors: | Jean-François Burnol |
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Institution: | Université Lille 1, UFR de mathématiques, cité scientifique M2, 59655 Villeneuve d''Ascq cedex, France |
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Abstract: | Dyson has associated with the Fredholm determinants of the even (resp. odd) Dirichlet kernels a Schrödinger equation on the half-axis and has used, in tandem, the Gel'fand–Levitan and Marchenko methods of inverse scattering theory to study the asymptotics of these determinants. We have proposed following our unearthing of the conductor operator to seek to realize the Fourier transform itself as a scattering, and we obtain here to this end two Dirac systems on the entire real axis which are intrinsically associated, respectively, to the cosine and to the sine transforms. To cite this article: J.-F. Burnol, C. R. Acad. Sci. Paris, Ser. I 336 (2003). |
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