Introduction to the spectral theory of polynomial operator pencils. Transl. from the Russian by H. H. McFaden. (English) Zbl 0678.47005

Markus, A. S.

Translations of Mathematical Monographs, 71. Providence, RI: American Mathematical Society (AMS). iv, 250 p. $ 15.00 (1988).

This book is reviewed together with the Russian original below.

MSC:

47A56	Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47A70	(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47-02	Research exposition (monographs, survey articles) pertaining to operator theory
47A10	Spectrum, resolvent
47A55	Perturbation theory of linear operators
47A68	Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators

Keywords:

spectral theory of polynomial operator pencils; completeness of the system of generalized eigenvectors; convergence of eigenvector expansions; pencils with unbounded operator-coefficients; method of factorization; existence of spectral divisor; Krein-Langer theorem; spectral properties of the roots of some operator equations arising from factorization; variational methods for selfadjoint operator functions; quadratic hyperbolic pencils

Citations:

Zbl 0678.47006