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On positive functions with positive Fourier transforms

B. G. Giraud·R. Peschanski
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Abstract

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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BibTeXRIS

B. G. Giraud, R. Peschanski. 2005-04-05. On positive functions with positive Fourier transforms. https://arxiv.org/abs/math-ph/0504015

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