Related papers: Frame sets for generalized $B$-splines
We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection…
We investigate the completeness of Gabor systems with respect to several classes of window functions on rational lattices. Our main results show that the time-frequency shifts of every finite linear combination of Hermite functions with…
The relationship between the frame bounds of frames (Gabor) for the space $L^2(\mathbb{R})$ with several generators from the Weyl-Heisenberg group and the scalars linked to the sum of frames is examined in this paper. We give sufficient…
We propose a formal definition of a general reference frame in a general spacetime, as an equivalence class of charts. This formal definition corresponds with the notion of a reference frame as being a (fictitious) deformable body, but we…
We introduce a general framework for the construction of polynomial frames in $L^2(\mathbb{S}^{d-1})$, $d \geq 3$, where the frame functions are obtained as rotated versions of an initial sequence of polynomials $\Psi^j$, $j\in…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
In this paper, we introduce and study frame of operators in quaternionic Hilbert spaces as a generalization of g frames which in turn generalized various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion…
This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…
Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…
In this article we obtain families of frames for the space B_\omega of functions with band in [-\omega,\omega] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant,…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear…
Frames are the most natural generalization of orthonormal bases that allow the inclusion of redundant systems. In this article, we introduce the concept of frames generated by graphs in finite-dimensional spaces and study their properties.…
We construct Hilbert $C^*$-modules useful for studying Gabor systems and show that they are Banach algebras under pointwise multiplication. For rational $ab<1$ we prove that the set of functions $g \in L^2(R)$ so that $(g,a,b)$ is a Bessel…
We develop a formalism to study the use of Level Set Method (LSM) in the investigation of evolution of observables in terms of parameters of the Hamiltonian, both of the system itself and the control part. A simple example with an analytic…
Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower)…
Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
We characterize the normal operators $A$ on $\ell^2$ and the elements $a^i \in \ell^2$, with $1\le i\le m$, such that the sequence $$\{ A^n a^1 , \ldots , A^n a^m \}_{n\ge 0}$$ is a frame. The characterization makes strong use of the…