Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one

Alexander V. Sobolev

Type: Article

Publication Date: 2006-04-30

Citations: 15

DOI: https://doi.org/10.4171/rmi/449

Abstract

We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.

Locations

Revista Matemática Iberoamericana - View - PDF
Project Euclid (Cornell University) - View - PDF

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+	Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators	1987	M. M. Skriganov
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+ PDF Chat	ASYMPTOTIC EXPANSION OF THE STATE DENSITY AND THE SPECTRAL FUNCTION OF A HILL OPERATOR	1987	D. Shenk Mikhail Shubin
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+	Asymptotics of eigenvalue clusters for the Laplacian plus a potential	1977	Alan Weinstein
+	THE SPECTRAL THEORY AND THE INDEX OF ELLIPTIC OPERATORS WITH ALMOST PERIODIC COEFFICIENTS	1979	Mikhail Shubin