相关论文: Unitary systems, wavelet sets, and operator-theore…

A weighted composition operator on a reproducing kernel Hilbert space is given by a composition, followed by a multiplication. We study unitary and co-isometric weighted composition operators on unitarily invariant spaces on the Euclidean…

In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…

We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…

In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}(\mathbb{N}) \to H$, the analysis operator $T^{\ast}:H\to $ $% \ell ^{2}(\mathbb{N}) $ and the…

A frame in an $n$-dimensional Hilbert space $H_n$ is a possibly redundant collection of vectors $\{f_i\}_{i\in I}$ that span the space. A tight frame is a generalization of an orthonormal basis. A frame $\{f_i\}_{i\in I}$ is said to be…

We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…

As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…

Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra $A$ which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper we…

A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…

In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…

Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. In this paper, we study the notion of excess for woven…

Starting with an integrable unitary representation of a locally compact group and its associated voice transform, coorbit theory describes the construction and investigation of the so-called coorbit spaces. A coorbit space consists of…

We present two results on multiqubit Werner states, defined to be those states that are invariant under the collective action of any given single-qubit unitary that acts simultaneously on all the qubits. Motivated by the desire to…

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…