Related papers: Frame related operators for woven frames
The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in…
We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…
We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…
We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…
In this work, we consider some relationships between a closed range operator $T$ and a fusion frame $\mathcal{W}=(W_i,w_i)_{i\in I}$ for a Hilbert space $\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i)_{i\in I}$ is a…
In this paper, a new notion of frames is introduced: $\ast$-operator frame as generalization of $\ast$-frames in Hilbert $C^{\ast}$-modules introduced by A. Alijani and M. A. Dehghan \cite{Ali} and we establish some results.
Frames normal for linear connections in vector bundles are defined and studied. In particular, such frames exist at every fixed point and/or along injective path. Inertial frames for gauge fields are introduced and on this ground the…
A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…
This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance…
We extend Robertson's theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone's theorem and the theory of spectral multiplicity to analyze wandering frame…
This paper studies frames in Hilbert spaces generated by the orbits of (in)-finitely many vectors under a single operator, presenting new results on multiplication operators and operators composed of Jordan blocks, which generalizes…
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in…
Boundary operators are gauge invariant operators whose form factors correspond to boundary contributions of BCFW shifts. In gauge theory, the boundary operators contain infinite series, which are constrained by gauge symmetry. We compute…
Algebraic framework for construction of a commuting set of operators that can be interpreted as integrals of motion of the open spin chain with boundary conditions and nearest neighbour interaction is investigated.
This paper initiates a systematic study of operators arising as integrals of operator-valued functions with respect to positive operator-valued measures and utilizes these tools to provide relativization maps (Yen) for quantum reference…
In this paper we study frame-like properties of a wave packet system by using hyponormal operators on $L^2(\mathbb{R})$. We present necessary and sufficient conditions in terms of relative hyponormality of operators for a system to be a…
We consider sequences in a Hilbert space $\mathcal H$ of the form $(T^nf_0)_{n\in I},$ with a linear operator $T$, the index set being either $I = \mathbb N$ or $I = \mathbb Z$, a vector $f_0\in \mathcal H$, and answer the following two…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…