Related papers: Pairs of Woven continuous frames in Hilbert spaces
Generalized fusion frame and some of their properties in tensor product of Hilbert spaces are described. Also, the canonical dual g-fusion frame in tensor product of Hilbert spaces is considered. Finally, the frame operator for a pair of…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…
In this paper we consider on the notion of continuous frame of subspace and define a new concept of continuous frame, entitled {\it continuous atomic resolution of identity}, for arbitrary Hilbert space $\h$ which has a countable…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…
Weaving frames have potential applications in wireless sensor networks that require distributed processing of signal under different frames. In this paper, we study some new properties of weaving generalized frames (or $g$-frames) and…
Our main goal in this paper, is to generalize to Hilbert C*-modules the concept of fusion frames. Indeed we introduce the notion of *\~nfusion frames associated to weighted sequences of orthogonally complemented submodules of a Hilbert…
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 paper we introduce and investigate the concept of repro- ducing pairs as a generalization of continuous frames. Reproducing pairs yield a bounded analysis and synthesis process while the frame condition can be omitted at both…
In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.
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…
This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to…
After introducing g-frames and fusion frames by Sun and Casazza, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give…
We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the…