0 Ju n 20 04 FOURIER TRANSFORMS IN EXPONENTIAL REARRANGEMENT INVARIANT SPACES

A Hausdorff-young Theorem for Rearrangement-invariant Spaces

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 ^ V ̂ 2, p~ + q= 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p~ι9 it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to ςr such that the Fourier transform is a bounded linear operator from X...

Shift-Invariant Spaces and Linear Operator Equations

In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier transforms and semi-convolutions are used to characterize shift-invariant spaces. Criteria are provided for solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The results are then ap...

The Paley-wiener Theorem and the Local Huygens’ Principle for Compact Symmetric Spaces

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new proofs of the strong Huygens’ principle for a suitable constant shift of the w...

EXPONENTIAL MAP OF A CLASS OF TOP SPACES

Wavelet transforms on Gelfand-Shilov spaces and concrete examples

In this paper, we study the continuity properties of wavelet transforms in the Gelfand-Shilov spaces with the use of a vanishing moment condition. Moreover, we also compute the Fourier transforms and the wavelet transforms of concrete functions in the Gelfand-Shilov spaces.