Vladimir GEORGESCU, Andrei IFTIMOVICI
Riesz-Kolmogorov Compacity Criterion, Ruelle Theorem 
and Lorentz Convergence on Locally Compact Abelian Groups
(296K, Postscript)

ABSTRACT.  We prove a version of Ruelle's theorem (concerning the description of 
the pure point and continuous spectral subspaces of a hamiltonian in 
terms of bound and scattering states) valid for an arbitrary 
self-adjoint operator $H$ in $L^2(X)$, the configuration space $X$ 
being an arbitrary abelian locally compact group. This version follows 
from the Riesz-Kolmogorov theorem which, in our presentation, gives a 
description of relatively compact sets of states solely in terms of 
phase space properties of the system. We also replace in Ruelle's 
theorem the convergence in the Ces\`aro mean by convergence 
in Lorentz sense, which is sharper than any convergence in the mean.