A Remainder Estimate for Weyl’s Law on Liouville Tori
نویسنده
چکیده
Abstract. The Liouville tori, having an integrable metric of the form (U1(q1)− U2(q2))(dq 2 1 + dq 2 ), allow the separation of variables in the study of the Laplacian spectrum. The asymptotic analysis of the resulting Sturm-Liouville problems allows to reduce the count of the eigenvalues of the spectrum to the count of the lattice points inside a plane domain. The present paper is concerned with the remainder in the Weyl’s law. It is shown that, under specified conditions, a Liouville torus has a remainder of order O(λ). Colin de Verdière previously obtained this bound for a generic surface of revolution, also a surface with integrable metric.
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تاریخ انتشار 2009