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

Victor Ivrii ()
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Victor Ivrii: University of Toronto, Department of Mathematics

Chapter Chapter 34 in Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 2019, pp 583-606 from Springer

Abstract: 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(x, hD) 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.

Keywords: Microlocal Analysis; sharp spectral asymptotics; integrated density of states; periodic and almost periodic operators; Diophantine conditions; 35P20 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-30561-1_34

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DOI: 10.1007/978-3-030-30561-1_34

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