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Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics

Authors:

Yu G Safarov

Abstract:

Let

_j be the eigenvalues of a positive elliptic pseudodifferential operator of order m > 0 on a closed compact d-dimensional C-manifold and let N( lambda

)=#{j:

^m}. It is shown that for each epsiv

> 0 we have

$\begin{gathered} c_0 (\lambda + \varepsilon )^d + c_1 \lambda ^{d - 1} + Q(\lambda + \varepsilon )\lambda ^{d - 1} + 0(\lambda ^{d - 1} ) \geqslant N(\lambda ) \geqslant \hfill \\ \geqslant c_0 (\lambda - \varepsilon )^d + c_1 \lambda ^{d - 1} + Q(\lambda - \varepsilon )\lambda ^{d - 1} + 0(\lambda ^{d - 1} ), \hfill \\ \end{gathered}$

Keywords:
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