Related papers: Hilbert-Schmidt Operators and Frames - Classificat…
In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs).…
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept…
We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…
Controlled frames have been recently introduced in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper, unlike the cross-Gram matrix of two different sequences which…
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…
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…
We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea…
The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also,…
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…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
Frames and orthonormal bases are naturally linked to bounded operators. To tackle unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
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…
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…
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…