We investigate vector-valued Gabor frames (sometimes called Gabor superframes) based on Hermite functions Hn. Let h = (H0, H1, . . . , Hn) be the vector of the first n+ 1 Hermite functions. We give a complete characterization of all lattices Λ ⊆ R such that the Gabor system {e2πiλ2th(t − λ1) : λ = (λ1, λ2) ∈ Λ} is a frame for L(R,C). As a corollary we obtain sufficient conditions for a single H...

The properties of the discrete Gabor scheme are considered in the context of oversampling. The approach is based on the concept of frames and utilizes the piecewise finite Zak transform (PFZT). The frame operator is represented as a matrix-valued function in the PFZT domain, and its properties are examined in relation to this function. The frame hounds are calculated by means of the eigenvalues...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

Title of dissertation: FRAME MULTIPLICATION THEORY FOR VECTOR-VALUED HARMONIC ANALYSIS Travis D. Andrews, Doctor of Philosophy, 2014 Dissertation directed by: Professor John J. Benedetto Department of Mathematics A tight frame Φ is a sequence in a separable Hilbert space H satisfying the frame inequality with equal upper and lower bounds and possessing a simple reconstruction formula. We define...

This article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups, includes some characterization theorems, and presents the uniformizability of stratified neighborhood topological groups within the unified approach of Gutiérrez García, DePrada Vicente, and Šostak. It is shown that for a frame L, the category L-NGrp is topologi...

One severe problem in frame-based description languages in that computing subsumytion in computationally intractable for languages of reasonable expressive power. Several partial solutions to this problem are used in knowledge representation systems that incorporate such languages, but none of these solutions are satisfactory if the system is to be of general use in representing knowledge. A ne...