2,905 research outputs found
On the remainder in the Weyl formula for the Euclidean disk
We prove a 2-terms Weyl formula for the counting function N(mu) of the
spectrum of the Laplace operator in the Euclidean disk with a sharp remainder
estimate O(mu^2/3)
Semi-classical trace formulas and heat expansions
in the recent paper [Journal of Physics A, 43474-0288 (2011)], B. Helffer and
R. Purice compute the second term of a semi-classical trace formula for a
Schr\"odinger operator with magnetic field. We show how to recover their
formula by using the methods developped by the geometers in the seventies for
the heat expansions.Comment: To appear in "Analysis of Partial Differential Equations
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