99-290 Jonathan D. Butler
Semi-Classical Counting Function with Application to Quantum Current (71K, AMS-TeX) Jul 30, 99
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Abstract. By adapting methods developed in a book by Yu. Safarov and D. Vassiliev to the semi-classical situation we obtain a new two-term asymptotic formula for the counting function of eigenvalues of $ h $ pseudodifferential operators in the limit as $ h \to 0 $. Recent results on clustering of eigenvalues obtained by V. Petkov and G. Popov follow in Corollary and, as an application, we consider the semi-classical behaviour of the quantum current studied recently by S. Fournais.

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