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

Alexander V. Sobolev

Revista Matemática Iberoamericana (2006)

  • Volume: 22, Issue: 1, page 55-92
  • ISSN: 0213-2230

Abstract

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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.

How to cite

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Sobolev, Alexander V.. "Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.." Revista Matemática Iberoamericana 22.1 (2006): 55-92. <http://eudml.org/doc/41965>.

@article{Sobolev2006,
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.},
author = {Sobolev, Alexander V.},
journal = {Revista Matemática Iberoamericana},
keywords = {Operadores pseudodiferenciales; Operadores elípticos; Teoría de perturbación; Espectros; Teoría de operadores; spectral theory; Schrödinger type operators; density of states},
language = {eng},
number = {1},
pages = {55-92},
title = {Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.},
url = {http://eudml.org/doc/41965},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Sobolev, Alexander V.
TI - Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 1
SP - 55
EP - 92
AB - 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.
LA - eng
KW - Operadores pseudodiferenciales; Operadores elípticos; Teoría de perturbación; Espectros; Teoría de operadores; spectral theory; Schrödinger type operators; density of states
UR - http://eudml.org/doc/41965
ER -

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