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

TL;DR
This paper derives comprehensive semiclassical spectral asymptotics for scalar operators with periodic or almost periodic perturbations, advancing understanding of spectral functions and density of states in such settings.
Contribution
It provides a complete semiclassical asymptotic expansion for the spectral function and integrated density of states for operators with periodic or almost periodic perturbations.
Findings
Derived full semiclassical asymptotics of spectral function
Established asymptotics for integrated density of states
Extended results to more general cases
Abstract
Under certain assumptions we derive a complete semiclassical asymptotics of the spectral function for a scalar operator \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*} where is an elliptic operator and 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.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods
