Related papers: Classification of General Sequences by Frame-Relat…
Frames and orthonormal bases are naturally linked to bounded operators. To tackle unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also…
In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…
A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et. al. In the studying of frames, some operators like analysis, synthesis, Gram and frame operator play the central role. In this…
Controlled frames have been recently introduced in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper, unlike the cross-Gram matrix of two different sequences which…
In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}(\mathbb{N}) \to H$, the analysis operator $T^{\ast}:H\to $ $% \ell ^{2}(\mathbb{N}) $ and the…
In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this…
Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel…
In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs).…
For applications like the numerical solution of physical equations a discretization scheme for operators is necessary. Recently frames have been used for such an operator representation. In this paper, we apply fusion frames for this task.…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…
This paper is devoted to the study of eigen-sequences for some important operators acting on sequences. Using functional equations involving generating functions, we completely solve the problem of characterizing the fixed sequences for the…
The conditions for sequences $\{f_{k}\}_{k=1}^{\infty}$ and $\{g_{k}\}_{k=1}^{\infty}$ being Bessel sequences, frames or Riesz bases, can be expressed in terms of the so-called cross-Gram matrix. In this paper we investigate the cross-Gram…
The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…
We consider translates of functions in $L^2(\RRd)$ along an irregular set of points. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel sequence…
In this peaper we stady certain Bessel sequences $\left\{f_k\right\}_{k=1}^{\infty}$ in Hilbert C*- modules $\mathcal{H}$ for which operator $S$ defined by \ref{eq2} is of the form $\mathcal{T}+\xi I$, for some real number $\xi$ and a…
G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…
We investigate systems of the form $\{A^tg:g\in\mathcal{G},t\in[0,L]\}$ where $A \in B(\mathcal{H})$ is a normal operator in a separable Hilbert space $\mathcal{H}$, $\mathcal{G}\subset \mathcal{H}$ is a countable set, and $L$ is a positive…
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…