English
Related papers

Related papers: Controlled K-frames in Hilbert Spaces

200 papers

A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et. al. In the studying of frames, some operators like analysis, synthesis, Gram and frame operator play the central role. In this…

Functional Analysis · Mathematics 2018-08-16 Asghar Rahimi , Zahra Samadzadeh , Bayaz Daraby

Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the…

Functional Analysis · Mathematics 2024-01-03 Hafida Massit , Mohamed Rossafi , Choonkil Park

There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully…

Quantum Physics · Physics 2009-11-11 R. de la Madrid

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 the present paper we introduce the generalized inverse operators which have an interesting role in operator theory. We establish Douglas' factorization theorem type for Hilbert pro-$C^{\ast}$-module. We introduce the notion of atomic…

Functional Analysis · Mathematics 2022-12-05 Mohamed Rossafi , Roumaissae Eljazzar , Ram Mohapatra

In this work, we provide some constructions and the sum of new continuous K-g-frames in Hilbert$C^{\ast}$-Modules. We provide certain necessary and sufficient conditions for some adjointable operators on $\mathcal{H}$, under which new…

Functional Analysis · Mathematics 2024-02-06 Abdelilah Karara , Mohamed Rossafi , Mohammed Klilou , Samir Kabbaj

We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct…

Functional Analysis · Mathematics 2024-04-08 Prasenjit Ghosh

We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…

Functional Analysis · Mathematics 2023-09-15 Prasenjit Ghosh , T. K. Samanta

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…

Functional Analysis · Mathematics 2023-10-31 Rosario Corso

Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. We demonstrate in this paper a representation theory for frames generated by operator…

Functional Analysis · Mathematics 2024-09-24 Chad Berner , Eric S. Weber

In this paper, our aim is to introduce the concept of a frame in n-Hilbert space and describe some of their properties. We further discuss tight frame relative to n-Hilbert space. At the end, we study the relationship between frame and…

Functional Analysis · Mathematics 2021-09-09 Prasenjit Ghosh , T. K. Samanta

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,…

Numerical Analysis · Mathematics 2020-07-08 Ben Adcock , Mohsen Seifi

G-fusion frames which are obtained from the combination of g-frames and fusion frames were recently introduced for Hilbert spaces. In this paper, we present a new identity for g-frames which was given by Najati in a special case. Also, by…

Functional Analysis · Mathematics 2018-06-12 Ramazan Zarghami , Vahid Sadri , Reza Ahmadi

In this paper, we present the concept of continuous biframes in a Hilbert space. We examine the essential properties of biframes with an emphasis on the biframe operator. Moreover, we introduce a new type of Riesz bases, referred to as…

Functional Analysis · Mathematics 2023-12-13 Hafida Massit , Roumaissae Eljazzar , Mohamed Rossafi

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

Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower)…

Functional Analysis · Mathematics 2012-05-31 Jean-Pierre Antoine , Peter Balazs

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

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

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

In this paper, we introduce the concept of Continuous $\ast$-K-g-Frame in Hilbert $C^{\ast}$-Modules and we give some properties.

Operator Algebras · Mathematics 2019-09-17 Abdeslam Touri , Mohamed Rossafi , Hatim Labrigui , Abdellatif Akhlidj