Jonathan D. Butler
Semi-Classical Counting Function with Application to Quantum Current
(71K, AMS-TeX)

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.