During the last several years, frames have become increasingly popular; they have
appeared in a large number of applications, and several concrete constructions of frames of …

Affine systems are reproducing systems of the form which arise by applying lattice
translation operators Tk to one or more generators ψℓ in L2 (Rn), followed by the application …

Abstract The Density Theorem for Gabor Frames is one of the fundamental results of time-
frequency analysis. This expository survey attempts to reconstruct the long and very involved …

We introduce a new concept to describe the localization of frames. In our main result we
show that the frame operator preserves this localization and that the dual frame possesses …

In this article, we develop a general method for constructing wavelets [Formula: see text] on
irregular lattices of the form X={xj, k∈ Rd: j∈ J, k∈ K}, and with an arbitrary countable family …

A wavelet with composite dilations is a function generating an orthonormal basis or a
Parseval frame for $ L^ 2 ({\mathbb R}^ n) $ under the action of lattice translations and …

This review chapter aims to strengthen the link between frame theory and signal processing
tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented …

We characterize orthonormal bases, Riesz bases and frames which arise from the action of
a countable discrete group Γ on a single element ψ of a given Hilbert space H. As Γ might …

The traditional study of reproducing systems involves the Gabor systems, that are generated
by the action of translations and modulations on a single or finite family of functions in L2 …

Abstract Extending work by Hernandez, Labate and Weiss, we present a sufficent condition
for a generalized shift-invariant system to be a Bessel sequence or even a frame for …