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Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition. (English. Russian original) Zbl 0679.35074

Funct. Anal. Appl. 22, No. 3, 213-223 (1988); translation from Funkts. Anal. Prilozh. 22, No. 3, 53-65 (1988).
The second term of the asymptotics of the spectral function of positive pseudodifferential operator on the closed manifold without nontrapping condition is obtained.
Reviewer: M.A.Perelmuter

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
58J40 Pseudodifferential and Fourier integral operators on manifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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