GENERAL RELATIVITY AND WEYL FRAMES

Eigenvalues of the Weyl Operator as Observables of General Relativity

We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as gravitational variables, and derive explicit formulas for their Poisson brackets and their time evolution. P.A.C.S. number:+04.20,04.90 On leave from Dipartimento di Fi...

A Necessary Condition for Weyl-Heisenberg Frames

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Relativity in rotating frames

A common error, originally due to Ehrenfest, is corrected. Typeset using REVTEX 1 A recent book [1] with the same title as above contains 17 articles by various authors, following the English translation of a brief note by Paul Ehrenfest [2] who applied a Lorentz contraction to the rim of a rotating disk, whose radius was not contracted. This is plainly wrong: Lorentz contractions occur when we...

Perturbations of Weyl-heisenberg Frames

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,...