Average Decay of the Fourier Transform

  • Giancarlo Travaglini
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


The aim of this paper is to describe some recent results and applications of the spherical L p average decay of the Fourier transform of measures or characteristic functions of convex bodies. We first focus on the different results depending on the indices ñ and on the shapes of the bodies. We then consider applications to geometric number theory and to irreg-ularities of distributions, as well as to generalized Radon transforms. The results are mostly known and they are described in the 2-dimensional case, even when extensions to several variables are known to be true.


Lattice Point Convex Body Positive Curvature Diophantine Approximation Lebesgue Constant 


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Giancarlo Travaglini
    • 1
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly

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