97-63 Bleher P.

Trace Formula for Quantum Integrable Systems, Lattice-Point 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 point-problem in convex and nonconvex domains, trace formula, and a related problem of small divisors. This includes the following subjects: (i) Semiclassical quantization by Einstein-Brillouin-Keller and the problem of completeness of semiclassical eigenfunctions. (ii) The lattice-point problem. (iii) The Gutzwiller-Berry-Tabor trace formula for quantum integrable systems. (iv) The problem of small divisors. (v) The saturation phenomenon.

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