Compactly supported smooth piecewise polynomial functions provide an efficient tool for the
approximation of curves and surfaces and other smooth functions of one and several …

A simple characterization is given of finitely generated subspaces of L 2 (R d) which are
invariant under translation by any (multi) integer, and is used to give conditions under which …

As a rapidly growing, multidisciplinary field of mathematics, wavelet theory provides the
major mathematical multiscale representation for analyzing functions/data and has …

We study basic questions of wavelet decompositions associated with multiresolution
analysis. A rather complete analysis of multiresolution associated with the solution of a …

A convenient setting for studyingmultiscale techniquesin various areas of applications is
usually based on a sequence of nested closed subspaces of some function space script F …

Subdivision schemes play an important role in computer graphics and wavelet analysis. In
this paper we are mainly concerned with convergence of subdivision schemes in L p spaces …

We investigate linear independence of integer translates of a finite number of compactly
supported functions in two cases. In the first case there are no restrictions on the coefficients …

Wavelet decompositions are based on basis functions satisfying refinement equations. The
stability, linear independence, and orthogonality of the integer translates of basis functions …

In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-
valued signals living in a shift-invariant space from their phaseless samples taken either on …

The local reconstruction from samples is one of most desirable properties for many
applications in signal processing, but it has not been given as much attention. In this paper …