Spectral theory of ordinary differential operators. (English) Zbl 0647.47052

Lecture Notes in Mathematics, 1258. Berlin etc.: Springer-Verlag. VI, 303 p.; DM 50.00 (1987).
The author’s intention is to provide a general and rather complete theory of self-adjoint ordinary differential operators of arbitrary order n operating on \({\mathbb{C}}^ m\)-valued functions, m being an arbitrary natural number; and to apply this theory to Sturm-Liouville operators and Dirac systems, paying special attention to oscillation theory and absolute continuity of the spectrum. He has succeeded in producing an attractive, compact volume which is virtually self-contained and should be of considerable interest to the large number of mathematicians with interests in spectral theory ans.


47E05 General theory of ordinary differential operators
47A10 Spectrum, resolvent
34L99 Ordinary differential operators
47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
47-02 Research exposition (monographs, survey articles) pertaining to operator theory