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Asymptotics of the spectrum of pseudo-differential operators with small parameters. (Russian) Zbl 0534.35075
The author obtains asymptotics of the distribution of eigenvalues, as \(\epsilon\to 0\), of pseudo-differential operators \[ L(\epsilon,h)\equiv \epsilon^{m_ 0}A_ 0f+\sum^{\ell}_{j=1}h_ j\epsilon^{m_ j}A_ jf=\lambda f, \] where \(A_ K\), \(K=0,1,...,\ell\), are classical scalar symmetric pseudo-differential operators and \(\epsilon>0\), \(h_ j\), \(j=1,...,\ell\), are small real parameters satisfying \(| h_ j| \leq C_ j\epsilon^{1/p},j=1,2,...,\ell,\) with natural p and constants \(C_ j\).
Reviewer: P.C.Sinha

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35B20 Perturbations in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
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