Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-19T08:49:43.119Z Has data issue: false hasContentIssue false

Spectral functions of a symmetric linear relation with a directing mapping, II

Published online by Cambridge University Press:  14 November 2011

H. Langer
Affiliation:
Sektion Mathematik, Technische Universität Dresden, G.D.R.
B. Textorius
Affiliation:
Department of Mathematics, University of Linköping, Sweden

Synopsis

The results of part I (see [5]) are applied to pairs of formally symmetric differential expressions, to Hermitian differential systems and to a reduced operator moment problem.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bennewitz, C.. Spectral theory for hermitean differential systems. International Conference on Spectral Theory of Differential Operators, Birmingham, Alabama, 1981 (Amsterdam: North Holland, 1981).Google Scholar
2Coddington, E. A. and Snoo, H. S. V. de. Differential subspaces associated with pairs of ordinary differential expressions. J. Differential Equations 35 (1980), 129182.CrossRefGoogle Scholar
3Dijksma, A. and H. S. V. de Snoo. Eigenfunction expansions associated with pairs of ordinary differential expressions. J. Differential Equations (submitted).Google Scholar
4Langer, H.. Über die Methode der richtenden Funktionale von M. G. Krein. Acta Math. Acad. Sci. Hungar. 21 (1970), 207224.CrossRefGoogle Scholar
5Langer, H. and Textorius, B.. Spectral functions of a symmetric linear relation with a directing mapping, I. Proc. Roy. Soc. Edinburgh Sect. A 97 (1984), 165176.CrossRefGoogle Scholar
6Langer, H. and Textorius, B.. L-resolvent matrices of symmetric linear relations with equal defect numbers; applications to canonical differential relations. Integral Equations Operator Theory 5 (1982), 208243.CrossRefGoogle Scholar
7Langer, H. and Textorius, B.. On generalized resolvents and Q-functions of symmetric linear relations (subspaces) in Hilbert space. Pacific J. Math. 72 (1977), 135165.CrossRefGoogle Scholar
8Naimark, M. A.. Linear Differential Operators (New York: Ungar, 1968).Google Scholar
9Schneider, A. und Niessen, H. D.. Links-definite singuläre kanonische Eigenwertprobleme. I. J. Reine Angew. Math. 281 (1976), 1352.Google Scholar
10Schneider, A. und Niessen, H. D.. Links-definite singuläre kanonische Eigenwertprobleme. II. J. Reine Angew. Math. 289 (1977) 6284.Google Scholar