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We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…
To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…
In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced…
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…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that…
Frames are the most natural generalization of orthonormal bases that allow the inclusion of redundant systems. In this article, we introduce the concept of frames generated by graphs in finite-dimensional spaces and study their properties.…
A new class of operators, larger than $C$-symmetric operators and different than normal one, named $C$--normal operators is introduced. Basic properties are given. Characterizations of this operators in finite dimensional spaces using a…
We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that -- is a frame for H, for some -- . We state a necessary condition in order for a frame -- to have a…
We consider a family of gradient Gaussian vector fields on $\Z^d$, where the covariance operator is not translation invariant. A uniform finite range decomposition of the corresponding covariance operators is proven, i.e., the covariance…
This paper examines the construction and properties of binary Parseval frames. We address two questions: When does a binary Parseval frame have a complementary Parseval frame? Which binary symmetric idempotent matrices are Gram matrices of…
We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
In this Work, We introduce the concept of $\ast$-operator frame, which is a generalization of $\ast$-frames in Hilbert pro-$C^{\ast}$-modules, and we establish some results, we also study the tensor product of $\ast$-operator frame for…
One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
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…