On positive functions with positive Fourier transforms

Details On positive functions with positive Fourier transforms On positive functions with positive Fourier transforms

2005-04-05

arxiv.org/abs/math-ph/0504015v1

ActaPhys.Polon.B37:331-346,2006

Physics

Mathematical Physics

12 pages, 23 figures. High definition figures can be obtained upon request at giraud@dsm-mail.saclay.cea.fr or pesch@dsm-mail.

Scientific paper

Using 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.

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