On positive functions with positive Fourier transforms

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dc.creatorGiraud, B. G.
dc.creatorPeschanski, R.
dc.date2005-04-05
dc.date.accessioned2026-07-07T11:32:27Z
dc.date.available2026-07-07T11:32:27Z
dc.descriptionUsing the basis of Hermite-Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive the practical constraints for a function and its Fourier transform to be both positive. We propose a constructive method based on the algebra of Hermite polynomials. Applications are extended to the 2-dimensional case (i.e. Fourier-Bessel transforms and the algebra of Laguerre polynomials) and to adding constraints on derivatives, such as monotonicity or convexity.
dc.description12 pages, 23 figures. High definition figures can be obtained upon request at giraud@dsm-mail.saclay.cea.fr or pesch@dsm-mail.saclay.cea.fr
dc.identifierhttps://arxiv.org/abs/math-ph/0504015
dc.identifierhttp://arxiv.org/abs/math-ph/0504015
dc.identifierActaPhys.Polon.B37:331-346,2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197599
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectHigh Energy Physics - Theory
dc.subjectNuclear Theory
dc.titleOn positive functions with positive Fourier transforms
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