We carefully perform a Hamiltonian Dirac's constraint analysis of the $\ensuremath{\omega}=\ensuremath{-}\frac{3}{2}$ Brans-Dicke theory with Gibbons-Hawking-York boundary term. The Poisson brackets are computed via functional derivatives. After brief summary results for $\ensuremath{\omega}\ensuremath{\ne}\ensuremath{-}\frac{3}{2}$ case [G. Gionti S. J., Canonical addresses inequivalence betwe...

Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

Title of dissertation: FRAME MULTIPLICATION THEORY FOR VECTOR-VALUED HARMONIC ANALYSIS Travis D. Andrews, Doctor of Philosophy, 2014 Dissertation directed by: Professor John J. Benedetto Department of Mathematics A tight frame Φ is a sequence in a separable Hilbert space H satisfying the frame inequality with equal upper and lower bounds and possessing a simple reconstruction formula. We define...

Partial frames provide a rich context in which to do pointfree structured and unstructured topology. A small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. These axioms are sufficiently general to include as examples bounded distributive...

This document contains supplementary materials for the paper Frames and numerical approximation by B. Adcock & D. Huybrechs [3]. SM1 Example 1. Fourier frames for complex geometries Consider the frame (3.1) over a domain Ω ⊆ (−1, 1)d. SM1.1 The kernel of G We first characterize the kernel of the Gram operator: Proposition SM1.1. Let G be the Gram operator (2.7) of the frame (3.1). Then Ker(G) =...

Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce Bessel subfusion sequences and subfusion frames and we investigate the relationship between their operation. Also, the definition of the orthogonal complement of subfusion frames and the definition of the completion of Bessel fusion sequences are provided and several results related with these no...

for all f ∈ H . The constant A (respectively, B) is a lower (resp. upper) frame bound for the frame. One of the most important frames for applications, especially signal processing, are the Weyl-Heisenberg frames. For g ∈ L(R) we define the translation parameter a > 0 and the modulation parameter b > 0 by: Embg(t) = e , Tnag(t) = g(t− na). For g ∈ L(R) and a, b > 0, we say for short that (g, a,...

Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the ...

We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {Ei}i∈I of a Hilbert space K and a surjective T ∈ L(K,H) in order that {T (Ei)}i∈I is a frame of subspaces with respect to a computable sequence of weights. We also o...

Finite normalized tight frames are interesting because they provide decompositions in applications and some physical interpretations. In this article, we give a recursive method for constructing them.