Discrete affine systems are obtained by applying dilations to a given shift-invariant system.
The complicated structure of the affine system is due, first and foremost, to the fact that it is not …

A complete characterization is given of closed shift-invariant subspaces of ${L_2}({\mathbb {R}^
d}) $ which provide a specified approximation order. When such a space is principal (ie, …

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator Whenever
T is well-defined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is …

Identifying anomalies rapidly and accurately is critical to the efficient operation of large
computer networks. Accurately characterizing important classes of anomalies greatly facilitates …

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 …

A new approach for the construction of wavelets and prewavelets onR d from multiresolution
is presented. The method uses only properties of shift-invariant spaces and orthogonal …

We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis
on tight wavelet frames. In particular, we establish general principles and specific algorithms …

In a recent paper by Nira Dyn and the author, univariate cardinal exponential B-splines are
shown to have a representation similar to the wellknown box spline representation of the …

We provide a map which associates each finite set Θ in complexs-space with a polynomial
space π Θ from which interpolation to arbitrary data given at the points in Θ is possible and …

1.1. Frames, Riesz bases, and their dual systems. The present paper is the sec-ond in a series
of three, all devoted to the study of shift-invariant frames and shift-invariant stable (= Riesz…