From "Dirac combs" to Fourier-positivity

Understand

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.
• Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms.
• A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed.