On positive functions with positive Fourier transforms
Giraud, B. G. ; Peschanski, R.
arXiv, 0504015 / Harvested from arXiv
Text on arXiv
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 transform to be both 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.
Publié le : 2005-04-05
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  High Energy Physics - Phenomenology,  High Energy Physics - Theory,  Nuclear Theory 
@article{0504015,
     author = {Giraud, B. G. and Peschanski, R.},
     title = {On positive functions with positive Fourier transforms},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504015}
}

Giraud, B. G.; Peschanski, R. On positive functions with positive Fourier transforms. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504015/