 00520 Vladimir GEORGESCU, Andrei IFTIMOVICI
 RieszKolmogorov Compacity Criterion, Ruelle Theorem
and Lorentz Convergence on Locally Compact Abelian Groups
(296K, Postscript)
Dec 31, 00

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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
selfadjoint operator $H$ in $L^2(X)$, the configuration space $X$
being an arbitrary abelian locally compact group. This version follows
from the RieszKolmogorov 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.
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