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Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…

We present a theory of finite frames for subspaces of $\mathbb{C}^N$ . The definition of a subspace frame is given and results analogous to those from frame theory for $\mathbb{C}^N$ are proven.

Information Theory · Computer Science 2014-10-21 Matthew Hirn , David Widemann

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.

Functional Analysis · Mathematics 2024-11-27 H. Hedayatirad , T. L. Shateri

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 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

Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…

Functional Analysis · Mathematics 2018-01-12 Poonam Mantry , S. K. Kaushik

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

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

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

In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…

Functional Analysis · Mathematics 2025-04-18 Hemalatha M , P. Sam Johnson , Harikrishnan P. K

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…

Functional Analysis · Mathematics 2014-12-23 Eliahu Levy , Orr Shalit

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…

Functional Analysis · Mathematics 2024-02-15 Abdelilah Karara , Mohamed Rossafi

We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence.…

Functional Analysis · Mathematics 2025-08-29 Shayne Waldron

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…

Functional Analysis · Mathematics 2017-06-26 Anirudha Poria

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 apply Lax-Milgram theorem to characterize scalable and piecewise scalable frame in finite and infinite-dimensional Hilbert spaces. We also introduce a method for approximating the inverse frame operator using finite-dimensional linear…

Functional Analysis · Mathematics 2022-12-05 Laura De Carli , Pierluigi Vellucci

Frames play significant role in various areas of science and engineering. In this paper, we introduce the concepts of frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H, K})$ and their generalizations. Moreover, we obtain some new results for…

Operator Algebras · Mathematics 2019-07-05 Mohamed Rossafi , Samir Kabbaj

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…

Functional Analysis · Mathematics 2011-08-10 Raphael Gervais Lavoie , Louis Marchildon , Dominic Rochon

We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…

Functional Analysis · Mathematics 2024-03-07 Prasenjit Ghosh , T. K. Samanta

We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. We then prove that pseudo-dual frames…

Functional Analysis · Mathematics 2016-04-21 Damir Bakić , Tomislav Berić