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

Alexander V. Sobolev | Zendy

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

Author(s) -

Alexander V. Sobolev

Publication year - 2006

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/449

Subject(s) - dimension (graph theory) , mathematics , differential operator , differential (mechanical device) , elliptic operator , mathematical analysis , pure mathematics , physics , thermodynamics

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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