Related papers: Weaving Riesz Bases
In this paper, we give new characterizations of modular Riesz bases in Hilbert $C^*$-modules. We prove that modular Riesz bases share many properties with Riesz bases in Hilbert spaces. Moreover we show that there are also important…
This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…
Gavruta introduced $K$-frames for Hilbert spaces to study atomic systems with respect to a bounded linear operator. There are many differences between K-frames and standard frames, so we study weaving properties of K-frames. Two frames…
We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural…
We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Specifically, we establish that it is always possible to stably reconstruct a vector in an arbitrary Riesz basis from sufficiently many of its…
Recent research has shown that the properties of overcomplete Gabor frames and frames arising from shift-invariant systems form a precise match with certain conditions that are necessary for a frame in $L^2(\mathbf R)$ to have a…
Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept…
Aldroubi has shown how one can construct any frame $\gtu$ starting with one frame $\ftu $,using a bounded operator $U$ on $l^2(N)$. We study the overcompleteness of the frames in terms of properties of $U$. We also discuss perturbation of…
In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these…
Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular,…
In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the…
Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a…
We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…
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).…
This article explores the problem of modifying the subspaces of a fusion frame in order to construct a Parseval fusion frame. In this respect, the notion of scalability is extended to the fusion frame setting. Then, scalable fusion Riesz…
Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and…
In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will…
The paper is concerned with the completeness property of root functions of general boundary value problems for $n \times n$ first order systems of ordinary differential equations on a finite interval. In comparison with the recent paper…
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a…
In this paper we introduce concepts of disjoint, strongly disjoint and weakly disjoint continuous $g$-frames in Hilbert spaces and we get some equivalent conditions to these notions. We also construct a continuous g-frame by disjoint…