Fejer kernels for Fourier series on Tn and on compact Lie groups.
Representations of Jordan algebras and special functions
This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.
Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on and on compact Lie groups)
We study polyhedral Dirichlet kernels on the n-dimensional torus and we write a fairly simple formula which extends the one-dimensional identity . We prove sharp results for the Lebesgue constants and for the pointwise boundedness of polyhedral Dirichlet kernels; we apply our results and methods to approximation theory, to more general summability methods and to Fourier series on compact Lie groups, where we write an asymptotic formula for the Dirichlet kernels.
Rearrangement of coefficients of Fourier series on
Central Fourier Analysis for Lorentz Spaces on Compact Lie Groups.
Hardy-Lorentz spaces and expansions in eigenfunctions of the Laplace-Beltrami operator on compact manifolds
On sets of completely uniform convergence
An L¹ estimate for half-space discrepancy
Average decay of Fourier transforms and geometry of convex sets.
Let B be a convex body in R, with piecewise smooth boundary and let ^χ denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical L averages of ^χ 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.
Pointwise convergence of Fourier series on compact Lie groups
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