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We study N-term approximation for general families of sequence spaces, establishing sharp versions of Jackson and Bernstein inequalities. The sequence spaces used are adapted to provide characterizations of Triebel-Lizorkin and Besov spaces by means of wavelet-like systems using general dilation matrices, and thus they include spaces of anisotropic… (More)
We give characterizations of radial Fourier multipliers as acting on radial L functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L −L bounds we also characterize weak type inequalities and intermediate… (More)
We introduce new ideas to treat the problem of connectivity of wavelets. We develop a method which produces intermediate paths of Tight Frame Wavelets (TFW). Using this method we prove that a large class of TFW-s, with only mild conditions on their spectrum, are arcwise connected.
We prove optimal embeddings for nonlinear approximation spaces Aq , in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for N -term wavelet approximation in L, Orlicz, and Lorentz norms. We also study the “greedy classes” G α q introduced by Gribonval… (More)
We adapt the proof for �(L) Wolff inequalities in the case of plate decompositions of paraboloids, to obtain stronger �2(Lp) versions. These are motivated by the study of Bergman projections for tube domains.
In this paper, we pursue the study of the radar ambiguity problem started in [Ja, GJP]. More precisely, for a given function u we ask for all functions v (called ambiguity partners) such that the ambiguity functions of u and v have same modulus. In some cases, v may be given by some elementary transformation of u and is then called a trivial partner of u… (More)
An important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp L results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite type curves in R and associated maximal functions. We observe that the… (More)
We observe that the range of p for Wolff’s inequality on plate decompositions of cone multipliers can be improved by using bilinear restriction techniques. This in turn is known to improve the range for sharp Lp results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones,… (More)
The material in this paper comes from various conferences given by the authors. We start with a brief survey of harmonic analysis methods in linear and non-linear approximation related to signal compression. Special emphasis is made on wavelet-based methods and some of the mathematical theory of wavelets behind them. We also present recent results of the… (More)
We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C logN . We show… (More)