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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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.

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

First available in Project Euclid: 24 May 2006

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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

periodic pseudodifferential operators density of states


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.

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