Related papers: Continuous K-biframes in Hilbert spaces
We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects and discuss some of the standard constructions from representation theory in this…
This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3,2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of…
After introducing a natural notion of continuous fields of locally convex spaces, we establish a new theory of strongly continuous families of possibly unbounded self-adjoint operators over varying Hilbert spaces. This setting allows to…
Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…
It is often inevitable to introduce an indefinite-metric space in quantum field theory. There is a problem to determine the metric structure of a given representation space of field operators. We show the systematic method to determine such…
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…
Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi…
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…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some…
Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in…
A definition of frames for Krein spaces is proposed, which extends the notion of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(\HH, \K{\,}{\,})$ is in particular a frame for $\HH$ in the Hilbert space sense. But it…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
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.…
In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…
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…