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

• Autores: Alexander V. Sobolev
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 1, 2006, págs. 55-92
• Idioma: español
• DOI: 10.4171/rmi/449
• Títulos paralelos:
  • Desarrollo asintótico de la densidad de estados integrada para operadores pseudodiferenciales elípticos periódicos en una dimensión
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• Resumen

  • 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.