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Pseudodifferential operators and spectral theory. Transl. from the Russian by Stig I. Andersson. 2nd ed. (English) Zbl 0980.35180
Berlin: Springer. xii, 288 p. (2001).
This book is the second edition of the well-known book by Shubin (1st English ed., Springer (1987; Zbl 0616.47040); Russian original, Nauka, Moskva (1978; Zbl 0451.47064)). The monograph occupies an exceptional place among books devoted to the theory of pseudodifferential operators, because it provides a rather simple presentation of main facts and deep results of the theory of pseudodifferential operators as well as Fourier integral operators.
The applications included in the books are: 1) Complex powers of elliptic operators, 2) Hörmander asymptotics of the spectral function and eigenfunctions, 3) Method of approximate spectral projection for asymptotics of eigenfunctions of elliptic pseudodifferential operators on $$\mathbb R ^n.$$
Appendix 1 is devoted to the wave fronts and propagation of singularities and Appendix 2 to quasiclassical asymptotic behavior of eigenfunctions of elliptic operators with parameter.

##### MSC:
 35S05 Pseudodifferential operators as generalizations of partial differential operators 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 47G30 Pseudodifferential operators 35S30 Fourier integral operators applied to PDEs 47-02 Research exposition (monographs, survey articles) pertaining to operator theory 35P20 Asymptotic distributions of eigenvalues in context of PDEs 58J40 Pseudodifferential and Fourier integral operators on manifolds