Indefinite Boundary Eigenvalue Problems in a Pontrjagin Space Setting

Results in Mathematics

Volumn 35, Issue 3-4, 1999, Pages 325-354

  Schneider, Albert ^a   Vonhoff, Rolf ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Eigenfunction expansions; Eigenvalue problems; Hamiltonian systems; Pontrjagin space

Indexed keywords

EID: 0007507925     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03322823     Document Type: Article

References (27)

1. T. Ya. Azizov and I. S. Iokhvidov: Linear Operators in Spaces with an Indefinite Metric, 1989
2. Branko Ćurgus and Heinz Langer: A Krein Space Approach to Symmetric Ordinary Differential Operators with an Indefinite Weight Function, Journal of Differential Equations, Vol. 79 (1989), pp. 31–61
3. Karim Daho and Heinz Langer: Sturm-Liouville Operators with an Indefinite Weight Function, Proceedings of the Royal Society of Edinburgh, Vol. 78 A (1977), pp. 161–191
4. Aad Dijksma, Heinz Langer and Henk de Snoo: Symmetric Sturm-Liouville Operators with Eigenvalue Depending Boundary Conditions, Canadian Mathematical Society Conference Proceedings, Vol. 8 (1987), Oscillation, Bifurcation and Chaos, pp. 87-116
5. Aad Dijksma, Heinz Langer and Henk de Snoo: Hamiltonian Systems with Eigenvalue Depending Boundary Conditions, Operator Theory: Advances and Applications, Vol. 35 (1988), pp. 37–83
6. W. Eberhard, G. Freiling and A. Schneider: On the Distribution of the Eigenvalues of a Class of Indefinite Eigenvalue Problems, Differential and Integral Equations, Vol. 3 (1990), pp. 1167–1179
7. Andreas Fleige: Full- and Half-Range-Entwicklungen für eine Klasse indefiniter Eigenwertprobleme Au = λTu, Diplomarbeit, Universität Dortmund 1991
8. Andreas Fleige: The “Turning Point Condition” of Beals for Indefinite Sturm-Liouville Problems, Mathematische Nachrichten, Vol. 172 (1995), pp. 109–112
9. Andreas Fleige: A Counterexample to Completeness Properties for Indefinite Sturm-Liouville Problems, Mathematische Nachrichten, Vol. 190 (1998), pp. 123–128
10. I. C. Gohberg and M. G. Krein: Introduction to the Theory of Linear Nonselfadjoint Operators, Providence, Rhode Island 1969
11. I. S. Iohvidov, M. G. Krein and H. Langer: Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric, Berlin 1982
12. Klaus Kopruch: Kanonische Rand-Eigenwertprobleme mit unstetigen Koeffizienten, Diplomarbeit, Universität Dortmund 1989
13. M. G. Krein: Theory of Self-Adjoint Extensions of Semi-Bounded Hermitian Operators and its Applications, I, Matematiceskij Sbornik 20 (62) (1947), pp. 431-495; II, Matematiceskij Sbornik 21(63) (1947), pp. 365–404 [in Russian with an English résumé]
14. Heinz Langer: Spectral Functions of Definitizable Operators in Krein Spaces, Lecture Notes in Mathematics 948 (1982), pp. 1–46
15. Heinz Langer, Reinhard Mennicken and Christiane Tretter: A Selfadjoint Linear Pencil Q — λP of Ordinary Differential Operators, Methods of Functional Analysis and Topology, Vol. 2 (1996), pp. 38–54
16. Heinz Langer and Albert Schneider: On Spectral Properties of Regular Quasidefinite Pencils F — λG, Results in Mathematics, Vol. 19 (1991), pp. 89–109
17. Angelo B. Mingarelli: A Survey of the Regular Weighted Sturm-Liouville Problem — The Non-Definite Case, International Workshop on Applied Differential Equations, Beijing, China 1985, World Scientific, Edited by Xiao Shutie, Pu Fuquan (1986), pp. 109-137
18. M. A. Naimark: Linear Differential Operators, Part II, London 1968
19. Heinz-Dieter Niessen and Anton Zettl: The Friedrichs Extension of Regular Ordinary Differential Operators, Proceedings of the Royal Society of Edinburgh, Vol. 114 A (1990), pp. 229–236
20. S. G. Pyatkov: Certain Properties of Eigenfunctions of Linear Pencils, Mathematical Notes (A Translation of Matematicheskie Zametki), Volume 51 (1992), pp. 90–95
21. F. W. schäfke and A. Schneider: S-Hermitesche Rand-Eigenwertprobleme I, Mathematische Annalen, Vol. 162 (1965), pp. 9–26
22. F. W. schäfke and A. Schneider: S-Hermitesche Rand-Eigenwertprobleme II, Mathematische Annalen, Vol. 165 (1966), pp. 236–260
23. F. W. schäfke and A. Schneider: S-Hermitesche Rand-Eigenwertprobleme III, Mathematische Annalen, Vol. 177 (1968), pp. 67–94
24. Albert Schneider: Die Green’sche Matrix S-hermitescher Rand-Eigenwertprobleme im Normalfall, Mathematische Annalen, Vol. 180 (1969), pp. 307–312
25. Albert Schneider: On Spectral Theory for the Linear Selfadjoint Equation Fy = λGy, Lecture Notes in Mathematics 846 (1981), pp. 306–332
26. Hans Volkmer: Sturm-Liouville Problems with Indefinite Weights and Everitt’s Inequality, Proceedings of the Royal Society of Edinburgh, Vol. 126 A (1996), pp. 1097–1112
27. Rolf Vonhoff: Some Remarks on Left-Definite Hamiltonian Systems in the Regular Case, to appear in: Mathematische Nachrichten, Vol. 193 (1998)