On positive functions with positive fourier transforms

B.G. Giraud (1) , R. Peschanski (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Keywords: numbers: 0230Gp; 0230Mv; 0230Nw; 1238-t

Domains: Mathematical Physics [math-ph]

B.G. Giraud, R. Peschanski. On positive functions with positive fourier transforms. Acta Physica Polonica B, 2006, 37 (2), pp.331-346. ⟨cea-02889284⟩