Related papers: Duality for Frames in Krein Spaces
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…
In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by…
In this paper we introduce concepts of disjoint, strongly disjoint and weakly disjoint continuous $g$-frames in Hilbert spaces and we get some equivalent conditions to these notions. We also construct a continuous g-frame by disjoint…
Let $H$ be a finite Hopf algebra with $C_{H,H} = C_{H,H}^{-1}.$ The duality theorem is shown for $H$, i.e., $$ (R # H)# H^{\hat *} \cong R \otimes (H \bar \otimes H^{\hat *}) \hbox {as algebras in} {\cal C}.$$ Also, it is proved that the…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group.…
For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete. In an earlier paper…
Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was introduced in four-dimensional Maxwell-Einstein theories coupled to a non-linear sigma model of scalar fields. In this short…
This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and…
This is the author's second paper treating the double coset problem for classical groups. Let $G$ be an algebraic group over an algebraically closed field $K$. The double coset problem consists of classifying the pairs $H,J$ of closed…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
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…
A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between…
In this paper we establish a suprising fundamental identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.
We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative…
Open sets and compact saturated sets enjoy a perfect formal symmetry, at least for classes of spaces such as Stone spaces or spectral spaces. For larger classes of spaces, a perfect symmetry may not be available, although strong signs of it…
It is a classical result that, if a maximal symmetric operator $T$ in a Krein space $\mathcal{H}=\mathcal{H}^-[\oplus]\mathcal{H}^+$ has the property $\mathcal{H}^-\subseteq\mathcal{D}_T$, then the imaginary part of its eigenvalue $\lambda$…
Frames play significant role in signal and image processing, which leads to many applications in differents fields. In this paper we define the dual of $\ast$-operator frames and we show their propreties obtained in Hilbert…
The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are…
We describe a simple algebraic approach to several spectral duality results for integrable systems and illustrate the method for two types of examples: The Bertola-Eynard-Harnad spectral duality of the two-matrix model as well as the…