English
Related papers

Related papers: Computable g- Frames

200 papers

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

The notion of a K-frame in n-Hilbert space is presented and some of their characterizations are given. We verify that sum of two K-frames is also a K-frame in n-Hilbert space. Also, the concept of tight K-frame in n-Hilbert space is…

Functional Analysis · Mathematics 2021-02-11 Prasenjit Ghosh , Tapas Kumar Samanta

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

Few years ago G\u{a}vru\c{t}a gave the notions of $K$-frame and atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$ in order to decompose $\mathcal{R}(K)$, the range of $K$, with a frame-like expansion. These…

Functional Analysis · Mathematics 2020-01-01 Giorgia Bellomonte

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.

Operator Algebras · Mathematics 2019-01-15 H. Labrigui , A. Touri , S. Kabbaj

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form $\{T^i f_1\}_{i\in \mathbb{N}}$, where $f_1$ belongs to Hilbert space $\h$ and $T:\h\rightarrow\h$ belongs to certain classes of the…

Functional Analysis · Mathematics 2018-12-04 Yavar Khedmati , Fatemeh Ghobadzadeh

Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…

Functional Analysis · Mathematics 2019-09-20 Fahimeh Arabyani Neyshaburi , Ali Akbar Arefijamaal

A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The basic tools of frame theory are described in the formalism of Krein spaces. It is…

Functional Analysis · Mathematics 2013-04-10 Kevin Esmeral , Osmin Ferrer , Elmar Wagner

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

Classical Analysis and ODEs · Mathematics 2007-05-23 Palle E. T. Jorgensen

A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of…

Functional Analysis · Mathematics 2018-08-14 Asghar Rahimi , Zahra Samadzadeh , Bayaz Daraby

$K$-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled $K$-fusion frames, and we develop some results on the controlled $K$-fusion frames for…

Functional Analysis · Mathematics 2020-07-13 N. Assila , S. Kabbaj , B. Moalige

In this paper, we introduce controlled frames in Hilbert $C^*$-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert…

Operator Algebras · Mathematics 2017-05-02 Mehdi Rashidi-Kouchi , Asghar Rahimi

The main purpose is to introduce the so-called bicomplex (bc)-frames which is a special extension to bicomplex infinite Hilbert spaces of the classical frames. The crucial result is the characterization of bc-frames in terms of their…

Functional Analysis · Mathematics 2020-01-22 Aiad El Gourari , Allal Ghanmi , Mohammed Souid El Ainin

In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…

Functional Analysis · Mathematics 2019-01-15 Vahid Sadri , Reza Ahmadi , Gholamreza Rahimlou

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

The most fundamental notion for Hilbert space frames is the sequence of frame coefficients for a vector x in the space. Yet, we know little about the distribution of these coefficient sequences. In this paper, we make the first detailed…

Functional Analysis · Mathematics 2015-04-16 Kevin Brewster , Peter G. Casazza , Eric Pinkham , Lindsey Woodland

In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…

funct-an · Mathematics 2008-02-03 Fabio Bagarello

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…

Functional Analysis · Mathematics 2015-01-29 Palle Jorgensen , Feng Tian

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson