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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…

Functional Analysis · Mathematics 2018-02-13 Yavar Khedmati , Mohammad Reza Abdollahpour

Frame Theory has a great revolution for recent years. This Theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. The purpose of this paper is the introduction and the study of the new concept that of Continuous…

Functional Analysis · Mathematics 2020-07-08 Abdeslam Touri , Hatim Labrigui , Samir Kabbaj

The theory of dynamical frames evolved from practical problems in dynamical sampling where the initial state of a vector needs to be recovered from the space-time samples of evolutions of the vector. This leads to the investigation of…

Functional Analysis · Mathematics 2025-05-27 Victor Bailey , Deguang Han , Keri Kornelson , David Larson , Rui Liu

Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…

Functional Analysis · Mathematics 2025-08-04 Hari Krishan Malhotra , Manisha Chhillar , Lalit Kumar Vashisht

Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames…

Functional Analysis · Mathematics 2021-01-13 A. Touri

In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…

Numerical Analysis · Mathematics 2022-11-04 Simon Hubmer , Ronny Ramlau , Lukas Weissinger

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

Mathematical Physics · Physics 2017-02-23 M. Khokulan , K. Thirulogasanthar , S. Srisatkunarajah

Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…

Functional Analysis · Mathematics 2012-02-21 Thomas Hotz , Fabian J. E. Telschow

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…

Functional Analysis · Mathematics 2024-05-28 M. Firouzi Parizi , A. Alijani , M. A. Dehghan

In this note, following the theory of discrete frame perturbations in a complex Hilbert space, we examine perturbation of rank $n$ continuous frame, rank $n$ continuous Bessel family and rank $n$ continuous Riesz family in a non-commutative…

Functional Analysis · Mathematics 2019-05-24 M. Khokulan , K. Thirulogasanthar

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

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

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…

Functional Analysis · Mathematics 2008-04-09 Peter Balazs

We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship…

Functional Analysis · Mathematics 2024-03-07 Prasenjit Ghosh , Tapas Kumar Samanta

In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this…

Functional Analysis · Mathematics 2023-10-31 Giorgia Bellomonte , Rosario Corso

In this paper, we introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames.…

Functional Analysis · Mathematics 2020-11-06 Anirudha Poria

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…

Functional Analysis · Mathematics 2015-11-20 Michael Speckbacher , Peter Balazs

Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…

Functional Analysis · Mathematics 2016-08-09 Asghar Rahimi , Zahra Darvishi , Bayaz Daraby

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

We introduce the notion of continuous controlled g-fusion frame in Hilbert space which is the generalization of discrete controlled g-fusion frame and give an example. Some characterizations of continuous controlled g-fusion frame have been…

Functional Analysis · Mathematics 2021-10-22 Prasenjit Ghosh , T. K. Samanta