A survey of weighted polynomial approximation with exponential weights.
A survey on D-semiclassical orthogonal polynomials.
A survey on wavelet methods for (geo) applications.
Wavelets originated in 1980's for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1,+1] and scalar and vector spherical wavelets on the unit sphere 'Omega' are discussed in more detail.
A system of exponential functions with shift and the Kostyuchenko problem.
A Theory of Generalized Multiresolution Structure and Pseudoframes of Translates.
A transplantation theorem for ultraspherical polynomials at critical index
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with .
A unified approach to various orthogonalities
A uniform estimate for quartile operators.
There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...
A universal constant for exponential Riesz sequences.
A variant of compressed sensing.
A version of the law of large numbers
By the method of Rio [10], for a locally square integrable periodic function f, we prove for almost every x and t > 0.
A wavelet characterization for weighted Hardy spaces.
In this article we give a wavelet area integral characterization for weighted Hardy spaces Hp(ω), 0 < p < ∞, with ω ∈ A∞. Our wavelet characterization establishes the identification between Hp(ω) and T2p (ω), the weighted discrete tent space, for 0 < p < ∞ and ω ∈ A∞. This allows us to use all the results of tent spaces for weighted Hardy spaces. In particular, we obtain the isomorphism between Hp(ω) and the dual space of Hp'(ω), where 1< p < ∞ and 1/p +...
A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.
Abelova cena v roce 2017 udělena za teorii waveletů
Abelovu cenu za matematiku získal v roce 2017 francouzský matematik Yves Meyer za rozvoj teorie waveletů. V článku se seznámíme s jeho vědeckým životopisem, hlavní myšlenkou teorie waveletů a jejich použitím v praxi.
Absolute convergence of the double series of Fourier-Haar coefficients.
Accuracy of Several Multidimensional Refinable Distributions.
Adaptive convex optimization in Banach spaces: a multilevel approach
This is mainly a review paper, concerned with some applications of the concept of Nonlinear Approximation to adaptive convex minimization. At first, we recall the basic ideas and we compare linear to nonlinear approximation for three relevant families of bases used in practice: Fourier bases, finite element bases, wavelet bases. Next, we show how nonlinear approximation can be used to design rigorously justified and optimally efficient adaptive methods to solve abstract minimization problems in...
Adaptive density estimation under weak dependence
Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue's measure. [Donoho et al. Ann. Stat.24 (1996) 508–539] propose near-minimax estimators based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are...
Adaptive wavelet methods for saddle point problems
Adaptive wavelet methods for saddle point problems
Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator....