 9763 Bleher P.
 Trace Formula for Quantum Integrable Systems, LatticePoint Problem,
and Small Divisors
(68K, TeX)
Feb 11, 97

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Abstract. We review rigorous results concerning almost periodicity by
Besicovitch of the spectral function of quantum integrable systems,
lattice pointproblem in convex and nonconvex domains,
trace formula, and a related problem of small divisors. This includes
the following subjects:
(i) Semiclassical quantization by EinsteinBrillouinKeller and the
problem of completeness of semiclassical eigenfunctions.
(ii) The latticepoint problem.
(iii) The GutzwillerBerryTabor trace formula for quantum integrable
systems.
(iv) The problem of small divisors.
(v) The saturation phenomenon.
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