Related papers: Dynamical Frames and Hyperinvariant Subspaces
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…
We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. We then prove that pseudo-dual frames…
A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert…
We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case…
We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…
Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…
For any Dirac theory of quantum gravity governed by a set of well-defined quantum constraints, we discover a universal formula for the exact form of the evolution Hamiltonian operator in a variable quantum reference frame of our…
We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…