Spectral analysis of higher order differential operators I: General properties of the M-function

Autor(en): Remling, C
Stichwörter: HAMILTONIANS; Mathematics; POTENTIALS; RANK-ONE PERTURBATIONS; S-HERMITIAN SYSTEMS; TITCHMARSH-WEYL COEFFICIENTS
Erscheinungsdatum: 1998
Herausgeber: LONDON MATH SOC
Journal: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volumen: 58
Ausgabe: 2
Startseite: 367
Seitenende: 380
Zusammenfassung: 
As is well known, the classical Titchmarsh-Weyl m-function for second order differential operators admits a generalisation to considerably larger classes of differential equations. In the applications, however, the use of the general M-matrix often turns out to be rather cumbersome. The paper interprets the m-function in terms of Hilbert space notions, and shows that, in a sense that is made precise, the classical m-function can be recovered as a part of the more complicated one. Applications of this trick lead to results on spectral multiplicity and on stability properties of the spectrum.
ISSN: 00246107
DOI: 10.1112/S0024610798006474

Show full item record

Google ScholarTM

Check

Altmetric