Publisher Summary This chapter explains basic examples of wavelet methods in numerical
analysis. It introduces the approximations and shows show the way they are related to …

This is a survey of nonlinear approximation, especially that part of the subject which is
important in numerical computation. Nonlinear approximation means that the approximants …

This paper studies the regularity of solutions to boundary value problems for the Laplace
operator on Lipschitz domains R in Rd and its relationship with adaptive and other nonlinear …

We introduce a new form of nonlinear approximation called restricted approximation. It is a
generalization of n-term wavelet approximation in which a weight function is used to control …

In this paper, we are concerned with regularity analysis for solutions to nonlinear partial
differential equations. Many important practical problems are related with the p-Laplacian …

Decomposition systems for function spaces Page 1 STUDIA MATHEMATICA 157 (2) (2003)
Decomposition systems for function spaces by G. Kyriazis (Nicosia) Abstract. Let Θ := {θe I : e …

We use the scale of Besov spaces B^\alpha_ {\tau,\tau}(O),\alpha> 0, 1/\tau=\alpha/d+ 1/p, p
fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial …

The goal of this paper is to provide wavelet characterizations for anisotropic Besov spaces.
Depending on the anisotropy, appropriate biorthogonal tensor product bases are introduced …

For any integers p, n≥ 2 necessary and sufficient conditions are given for scaling filters with
pn many terms to generate a p-multiresolution analysis in L2 (R+). A method for constructing …

We consider approximation rates of sparsely connected deep rectified linear unit (ReLU)
and rectified power unit (RePU) neural networks for functions in Besov spaces B^q(L^p) in …