Composite wavelet bases for operator equations

Composite wavelet bases for operator equations

This paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit n-cube. These bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains. This covers also elliptic boundary value problems, although this study is primarily motivated by our previous analysis of wavelet me...

Adaptive Wavelet Algorithms for solving operator equations

Wavelet and Multiscale Methods for Operator Equations *

Operator - Like Wavelet Bases of L 2 ( R d )

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a stochastic model: signals are tempered distributions such that the application of a whitening (differential) operator results in a realization...

An optimal adaptive wavelet method - for strongly elliptic operator equations