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Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators

  • Victor IvriiEmail author
Chapter

Abstract

Under certain assumptions we derive a complete semiclassical asymptotics of the spectral function \(e_{h,\varepsilon }(x, x,\lambda )\) for a scalar operator
$$\begin{aligned} A_\varepsilon (x, hD)= A^0(hD) + \varepsilon B(x, hD), \end{aligned}$$
where \(A^0\) is an elliptic operator and B(xhD) is a periodic or almost periodic perturbation.

In particular, a complete semiclassical asymptotics of the integrated density of states also holds. Further, we consider generalizations.

Key words and phrases

Microlocal Analysis sharp spectral asymptotics integrated density of states periodic and almost periodic operators Diophantine conditions 

2010 Mathematics Subject Classification:

35P20 

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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