Let B be a convex body in R-2, with piecewise smooth boundary and let <(chi)over cap>(B) denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical L-p-averages of <(chi)over cap>(B) and we relate our analysis to a problem in the geometry of convex sets. As an application we obtain sharp results on the average number of integer lattice points in large bodies randomly positioned in the plane
Brandolini, L., Rigoli, M., & Travaglini, G. (1998). Average decay of Fourier transforms and geometry of convex sets. REVISTA MATEMATICA IBEROAMERICANA, 14(3), 519-560.
Citazione: | Brandolini, L., Rigoli, M., & Travaglini, G. (1998). Average decay of Fourier transforms and geometry of convex sets. REVISTA MATEMATICA IBEROAMERICANA, 14(3), 519-560. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | No |
Titolo: | Average decay of Fourier transforms and geometry of convex sets |
Autori: | Brandolini, L; Rigoli, M; Travaglini, G |
Autori: | |
Data di pubblicazione: | 1998 |
Lingua: | English |
Rivista: | REVISTA MATEMATICA IBEROAMERICANA |
Appare nelle tipologie: | 01 - Articolo su rivista |