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math-ph2015★ 3 cited
From "Dirac combs" to Fourier-positivity
Bertrand G. Giraud, Robi Peschanski
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms.…
math-ph2014★ 6 cited
On the positivity of Fourier transforms
Bertrand G. Giraud, Robi Peschanski
Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but the…
math-ph2005★ 8 cited
On positive functions with positive Fourier transforms
B. G. Giraud, R. Peschanski
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 tra…