Average decay of Fourier transforms and geometry of convex sets.

Brandolini, Luca, Rigoli, Marco, and Travaglini, Giancarlo. "Average decay of Fourier transforms and geometry of convex sets.." Revista Matemática Iberoamericana 14.3 (1998): 519-560. <http://eudml.org/doc/39557>.

@article{Brandolini1998,
abstract = {Let B be a convex body in R2, with piecewise smooth boundary and let ^χB denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical Lp averages of ^χB 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.},
author = {Brandolini, Luca, Rigoli, Marco, Travaglini, Giancarlo},
journal = {Revista Matemática Iberoamericana},
keywords = {Transformada de Fourier; Conjuntos convexos; Geometría plana; Estimación; Espacios LP; convex body; Fourier transform; decays; -averages},
language = {eng},
number = {3},
pages = {519-560},
title = {Average decay of Fourier transforms and geometry of convex sets.},
url = {http://eudml.org/doc/39557},
volume = {14},
year = {1998},
}

TY - JOUR
AU - Brandolini, Luca
AU - Rigoli, Marco
AU - Travaglini, Giancarlo
TI - Average decay of Fourier transforms and geometry of convex sets.
JO - Revista Matemática Iberoamericana
PY - 1998
VL - 14
IS - 3
SP - 519
EP - 560
AB - Let B be a convex body in R2, with piecewise smooth boundary and let ^χB denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical Lp averages of ^χB 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.
LA - eng
KW - Transformada de Fourier; Conjuntos convexos; Geometría plana; Estimación; Espacios LP; convex body; Fourier transform; decays; -averages
UR - http://eudml.org/doc/39557
ER -