Revista Matemática Iberoamericana

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

Alexander V. Sobolev

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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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 22, Number 1 (2006), 55-92.

Dates
First available in Project Euclid: 24 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1148492176

Mathematical Reviews number (MathSciNet)
MR2267313

Zentralblatt MATH identifier
1121.35149

Subjects
Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Secondary: 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords
periodic pseudodifferential operators density of states

Citation

Sobolev , Alexander V. Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one. Rev. Mat. Iberoamericana 22 (2006), no. 1, 55--92. https://projecteuclid.org/euclid.rmi/1148492176


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References

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