# Average decay of Fourier transforms and geometry of convex sets.

Luca Brandolini; Marco Rigoli; Giancarlo Travaglini

Revista Matemática Iberoamericana (1998)

- Volume: 14, Issue: 3, page 519-560
- ISSN: 0213-2230

## Access Full Article

top## Abstract

top## How to cite

topBrandolini, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.