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.

Average decay of Fourier transforms and geometry of convex sets

TRAVAGLINI, GIANCARLO
1998

Abstract

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
No
Articolo in rivista - Articolo scientifico
Scientifica
Fourier transform, convex sets
English
Brandolini, L., Rigoli, M., & Travaglini, G. (1998). Average decay of Fourier transforms and geometry of convex sets. REVISTA MATEMATICA IBEROAMERICANA, 14(3), 519-560.
Brandolini, L; Rigoli, M; Travaglini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/6072
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