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Related papers: Woven fusion frames in Hilbert spaces

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We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven…

Functional Analysis · Mathematics 2024-03-12 Prasenjit Ghosh , T. K. Samanta

In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $\sigma \subset I$, $\{f_i\}_{i \in \sigma} \cup \{g_i\}_{i \in…

Functional Analysis · Mathematics 2019-05-09 Animesh Bhandari , Saikat Mukherjee

This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is…

Functional Analysis · Mathematics 2024-11-15 Carlos Cabrelli , Ursula Molter , Felipe Negreira

In this note, we prove some results related to small perturbations of a frame for a Hilbert space $\mathcal{H}$ in order to have a woven pair for $\mathcal{H}$. Our results complete those known in the literature. In addition we study a…

Functional Analysis · Mathematics 2022-03-08 Pablo Calderón , Mariano Ruiz

Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…

Functional Analysis · Mathematics 2023-09-14 Tom Needham , Clayton Shonkwiler

Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame…

Information Theory · Computer Science 2013-01-23 Emily J. King

Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In…

Functional Analysis · Mathematics 2025-09-24 Avinash Bhardwaj , Animesh Bhandari

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…

Functional Analysis · Mathematics 2007-05-23 David R. Larson

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…

General Mathematics · Mathematics 2023-08-22 Nadia Assila , Samir Kabbaj , Hicham Zoubeir

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the…

Functional Analysis · Mathematics 2009-07-01 Robert Calderbank , Peter G. Casazza , Andreas Heinecke , Gitta Kutyniok , Ali Pezeshki

Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…

Functional Analysis · Mathematics 2021-12-10 Yuxiang Xu , Dongwei Li , Jinsong Leng

Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…

Functional Analysis · Mathematics 2017-06-23 Mozhgan Mohammadpour , Brian Tuomanen , Rajab Ali Kamyabi Gol

We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…

Classical Analysis and ODEs · Mathematics 2016-12-19 Sigrid B. Heineken , Patricia M. Morillas

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…

Functional Analysis · Mathematics 2011-11-08 Bill Moran , Stephen Howard , Doug Cochran

In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled…

Functional Analysis · Mathematics 2018-12-04 Reza Rezapour , Asghar Rahimi , E. Osgooei , Hossien Dehghan

Thye theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and much more, as well as being a fruitful area of research in abstract mathematics. In this…

Functional Analysis · Mathematics 2007-05-23 Peter G. Casazza

Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…

Functional Analysis · Mathematics 2024-07-09 Lukas Köhldorfer , Peter Balazs

In this paper we introduced the concept of continuous relay fusion frames in Hilbert spaces. And we define the dual frames for continuous relay fusion frames. Finally we study the perturbation probleme of continuous relay fusion frames.

Functional Analysis · Mathematics 2023-01-02 Fakhr-dine Nhari , Mohamed Rossafi

A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert…

Classical Analysis and ODEs · Mathematics 2016-12-20 Sigrid B. Heineken , Patricia M. Morillas

We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…

Functional Analysis · Mathematics 2011-11-10 Mariano A. Ruiz , Demetrio Stojanoff