Weyl function and spectral properties of self-adjoint extensions

Integral Equations and Operator Theory

Volumn 43, Issue 3, 2002, Pages 264-289

  Brasche, Johannes F ^a   Malamud, Mark ^b   Neidhardt, Hagen ^c  

^a Matematiska Institutionen   (Sweden)

^b DONETSK NATIONAL UNIVERSITY   (Ukraine)

^c WIAS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036434690     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01255563     Document Type: Article

References (33)

1. N.I. Achieser and I.M. Glasmann "Theorie der linearen Operatoren im Hilbertraum", Akademie-Verlag, Berlin 1975.
2. S. Albeverio, J.F. Brasche and H. Neidhardt, On inverse spectral theory for self-adjoint extensions, J. Funct. Anal. 154 (1998), 130-173.
3. N. Aronszajn, On a problem of Weyl in the theory of singular Sturm-Liouville equations, Amer. J. Math. 79 (1957), 597-610.
4. N. Aronszajn and W.F. Donoghue, On exponential representations of analytic functions, J. Analyse Math. 5 (1956), 321-388.
5. Ju.M. Berezanskii, "Expansion in eigenfunctions of self-adjoint operators", Naukova Dumka, Kiev 1965, Engl. transl., Amer. Math. Soc., Providence, R.I., 1968.
6. Ju.M. Berezanskii, "Expansion in eigenfunctions of self-adjoint operators", Naukova Dumka, Kiev 1965, Engl. transl., Amer. Math. Soc., Providence, R.I., 1968.
7. J.F. Brasche, "On spectra of self-adjoint extensions and generalized Schrödinger operators", Habilitationsschrift, Ruhr-Universität Bochum, 1995.
8. J.F. Brasche, On inverse spectral theory for self-adjoint extensions: Nowhere dense singular continuous spectra and Hausdorff dimension of spectra, J. Op. Theory 43 (2000), 145-169.
9. J.F. Brasche, M.M. Malamud and H. Neidhardt, Weyl function and singular continuous spectra of self-adjoint extensions, CMS Conference Proceedings, vol. 29 (2000), Providence: American Mathematical Society, 75-84.
10. J.F. Brasche and H. Neidhardt, On the absolutely continuous spectrum of self-adjoint extensions, J. Funct. Analysis 131 (1995), 364-385.
11. J.F. Brasche and H. Neidhardt, On the singular continuous spectrum of self-adjoint extensions, Math. Zeitschr. 222 (1996), 533-542.
12. J.F. Brasche, H. Neidhardt and J. Weidmann, On the point spectrum of self-adjoint extensions, Math. Zeitschr. 214 (1993), 343-355.
13. N. Dunford and J.T. Schwartz, "Linear operators. Part I: General Theory", John Wiley & Sons, New York 1988.
14. V.A. Derkach and M.M. Malamud, On the Weyl function and Hermitian operators with gaps, Dokl. AN SSSR 293, No. 5 (1987), 1041-1046.
15. V.A. Derkach and M.M. Malamud, Generalized resolvents and the boundary value problems for Hermitian operators with gaps, J. Funct. Anal. 95 (1991), 1-95.
16. V.A. Derkach and M.M. Malamud, The extension theory of Hermitian operators and the moment problem, J. Math. Sc. 73, No.2 (1995), 141-242.
17. W.F. Donoghue, A theorem of the Fatou type, Monatsh. Math. 67 (1963), 225-228.
18. W.F. Donoghue, On the perturbation of spectra, Commun. Pure Appl. Math. 18 (1965), 559-579.
19. F. Gesztesy and E. Tsekanovskii, On matrix-valued Herglotz functions, to appear in Math. Nachr.
20. F. Gesztesy, N.J. Kalton, K.A. Makarov and E. Tsekanovskii, Some applications of operator-valued Herglotz functions, to appear in Operator Theory: Advances and Applications, Birkhäuser, Basel.
21. J.B. Garnett, "Bounded analytic functions", Academic Press 1981.
22. V.I. Gorbachuk and M.L. Gorbachuk, "Boundary value problems for operator differential equations", Mathematics and Its Applications, Soviet Series 48, Dordrecht etc., Kluwer Academic Publishers (1991).
23. p-spaces", Cambridge University Press 1980.
24. M.G. Krein and H. Langer, On defect subspaces and generalized resolvents of Hermitian operator acting in Pontrjagyn space. Funktsional. Anal. i. Prilozhen 5, No. 3 (1971), 54-69, Engl. transl, in Functinal Anal. Appl. 5 (1971).
25. M.G. Krein and A.A. Nudel'man, "The Markov moment problem and extremal problems", Moscow 1973, Engl. transl. Amer. Math. Soc., Providence, RI, 1977.
26. M.G. Krein and A.A. Nudel'man, "The Markov moment problem and extremal problems", Moscow 1973, Engl. transl. Amer. Math. Soc., Providence, RI, 1977.
27. N.S. Naboko, Uniqueness theorems for operator-valued functions with positive imaginary part and the singular spectrum, Ark. Mat. 25 (1987), 115-140.
28. I.P. Natanson, "Theory of functions with real variables", Izd. Nauka, Moscow 1974.
29. M. Reed and B. Simon, "Methods of Modern Mathematical Physics IV: Analysis of Operators", Academic Press, New York 1978.
30. S. Saks, "Theory of integrals" (Second revised edition), Hafner Publishing Company, New York 1937.
31. H. Weyl, Über gewöhnliche lineare Differentialgleichungen mit singulären Stellen und ihre Eigenfunktionen, Göttinger Nachrichten (1909), 37-64.
32. H. Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann. 68 (1910), 220-269.
33. H. Weyl, Über gewöhnliche Differentialgleichungen mit singulären Stellen und ihre Eigenfunktionen, Göttinger Nachrichten (1910), 442-467.