Related papers: Gram matrix associated to controlled frames
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…
A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…
Frame Theory has a great revolution in recent years, this Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. The purpose of this paper is the introduction and the study of the concept of Controlled Continuous…
This work is devoted to the study of Bessel and Riesz systems of the type $\big\{L_{\gamma}\mathsf{f}\big\}_{\gamma\in \Gamma}$ obtained from the action of the left regular representation $L_{\gamma}$ of a discrete non abelian group…
In this note a review, some considerations and new results about maps with values in a distribution space and domain in a $\sigma$-finite measure space $X$, are obtained. In particular, it is a survey about Bessel, frames and bases (in…
The paper is devoted to continuous frames and Riesz bases in Hilbert C*-modules. we define a continuous Riesz basis for Hilbert C*-modules and give some results about them.
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…
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…
Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g-fusion frame…
The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric systems the cross gramian possesses a useful relation to the system's associated Hankel…
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…
A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas…
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…
Frames allow all elements of a Hilbert space to be reconstructed by inner product data in a stable manner. Recently, there is interest in relaxing the definition of frames to understand the implications for stable signal recovery. In this…
So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…
In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert $C^*$-modules. We extend the Casazza-Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert…
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…
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of…
In this paper we study the concept of controlled $\ast$-operator frmae for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$. Also we discuss characterizations of controlled $\ast$-operator frames and we give some properties