On the positivity of Fourier transforms

Understand

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 they are far from being exhaustive.
• We propose two constructive sets of necessary conditions for positivity of the Fourier transforms and test their ability of constraining the positivity domain.
• One uses analytic continuation and Jensen inequalities and the other deals with Toeplitz determinants and the Bochner theorem.