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Journal articles
On positive functions with positive fourier transforms
Abstract : Using the basis of Hermite–Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive constraints for a function and its Fourier transform to be both real and 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.
Cited literature [17 references]
https://hal-cea.archives-ouvertes.fr/cea-02889284
Contributor : Bruno Savelli Connect in order to contact the contributor
Submitted on : Friday, July 3, 2020 - 4:43:08 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:04 PM
Long-term archiving on: : Thursday, September 24, 2020 - 8:48:16 AM
Contributor : Bruno Savelli Connect in order to contact the contributor
Submitted on : Friday, July 3, 2020 - 4:43:08 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:04 PM
Long-term archiving on: : Thursday, September 24, 2020 - 8:48:16 AM
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