We introduce the concept of the modular function for a shiftinvariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and...

Let {Wi}i∈I be a (redundant) sequence of subspaces each being endowed with a weight vi, and let H be the closed linear span of the Wi’s, a composite Hilbert space. Provided that {(Wi, vi)}i∈I satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a fusion frame. These systems contain conventional frames as a special case, however they go far “beyond fra...

The relevance in sampling theory of U -invariant subspaces of a Hilbert space H, where U denotes a unitary operator on H, is nowadays a recognized fact. Indeed, shift-invariant subspaces of L(R) become a particular example; periodic extensions of finite signals provide also a remarkable example. As a consequence, the availability of an abstract U -sampling theory becomes a useful tool to handle...

The proof of non-existence for co-affine frames is extended from the one-dimensional setting [GLWW] to the case of expansive dilation matrices in Rd. The problem of identifying subspaces on which co-affine systems may admit frame-type inequalities is then considered. In the context of multiresolution analysis it is shown that frame-type inequalities may hold on certain fundamental subspaces of ...

We consider three-dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process generating joint conditions the geometric description frame. The corresponding differential operator is shown to be self-adjoint. In special case planar frames, decomposes into direct sum two operators, one coupling out-of-plane displacement angular (torsional) other in-plane with...

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : `2(X)! H : c 7! X

In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.

The problem of reconstructing a function from the magnitudes its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous [2]. On other hand, is always finite-dimensional settings. A prominent example such phase retrieval recovery signal modulus Gabor transform. In this paper, we st...

Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames. In traditional frame theory, one method for showing that unit norm tight frames exist is to characterize them as the minimizers of an energy functional, known as the frame potential. We generalize the frame potential to ...