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Jonathan D. Butler
Semi-Classical Counting Function with Application to Quantum Current
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.