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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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