Related papers: A brief introduction to Hilbert space frame theory…
In this paper, we will introduce the new concepts of continuous bi-g-frames and continuous K-bi-g-frame for Hilbert spaces. Then, we examine some characterizations properties with the help of a biframe operator. Finally, we investigate…
The notion of controlled frames for Hilbert spaces were introduced by Balazs, Antoine and Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Controlled Frame Theory has a great revolution in…
This report explains the basic theory and common terminology of quantum physics without assuming any knowledge of physics. It was written by a group of applied mathematicians while they were reading up on the subject. The intended audience…
In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of…
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and…
We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
In the present paper, we introduce the notion of $E$-$g$-frames for a separable Hilbert spaces $\mathcal H$, where $E$ is an invertible infinite matrix mapping on the Hilbert space $\mathop\oplus\limits_{n=1}^{\infty}\mathcal H_n$. We study…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
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…
After introducing g-frames and fusion frames by Sun and Casazza, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…