Giancarlo Travaglini

Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in Euclidean and non-Euclidean spaces

We shall prove an equiconvergence theorem between Fourier-Bessel expansions of functions in certain weighted Lebesgue spaces and the classical cosine Fourier expansions of suitable related functions. These weighted Lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce shag results for the pointwise almost everywhere convergence of Fourier integrals of radial functions in the Lorentz spaces L p,q (R n ). Also we shall briefly apply the above approach to the study of the harmonic analysis of radial functions on noneuclidean hyperbolic spaces

Bessel functions associated with representations of formally real Jordan algebras

Abstract We study Bessel functions on the symmetric cone associated with a special formally real Jordan algebra. We extend the classical results of radial Fourier analysis and we prove an asymptotic formula.

Average decay of Fourier transforms and geometry of convex sets

Let B be a convex body in R2, with piecewise smooth boundary and let ^?B denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical Lp averages of ^?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.

On the Koksma-Hlawka inequality

The classical Koksma Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma Hlawka type inequality which applies to piecewise smooth functions

Quadrature rules and distribution of points on manifolds

f\chi_{\Omega}

Norms of characters and Fourier series on compact Lie groups

, with

Convex curves, Radon transforms and convolution operators defined by singular measures

f

Fourier Analysis and Convexity

smooth and

A Koksma-Hlawka inequality for simplices

\Omega

AVERAGE DECAY ESTIMATES FOR FOURIER TRANSFORMS OF MEASURES SUPPORTED ON CURVES

a Borel subset of