Pseudodifferential operators and spectral theory. Transl. from the Russian by Stig I. Andersson. (English) Zbl 0616.47040

Shubin, M. A.

Berlin etc.: Springer-Verlag. X, 278 p. DM 148.00 (1987).

Only few books and monographs on pseudodifferential operators were available when the Russian edition of this book appeared in 1978, cf. Zbl 0451.47064. In the meantime, the literature is rather fast and still growing, see e.g. the books by S. Rempel and B.-W. Schulze [Index theory of elliptic boundary problems, (1982; Zbl 0504.35002)], M. Taylor [Pseudodifferential operators (1981; Zbl 0453.47026)], F. Trèves [Introduction to pseudo-differential and Fourier integral operators I/II, Plenum Press New York (1980; Zbl 0453.47027)], H. Kumano-go [Pseudo-differential operators (1982; Zbl 0489.35003)], V. Ivrij [Precise spectral asymptotics for elliptic operators, Lect. Notes Math. 1100 (1984; Zbl 0565.35002)], and, in particular, the outstanding monography by L. Hörmander [The analysis of linear partial differential operators I-IV, (1983-1985; Zbl 0601.35001; Zbl 0521.35002; Zbl 0521.35001)]. Nevertheless, M. A. Shubin’s book is still valuable and useful, especially in view of spectral theory applications.

Reviewer: J.Appell

MSC:

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

Keywords:

spectral theory

Citations:

Zbl 0451.47064; Zbl 0504.35002; Zbl 0453.47026; Zbl 0453.47027; Zbl 0489.35003; Zbl 0565.35002; Zbl 0601.35001; Zbl 0521.35002; Zbl 0521.35001