Abstract
For a class of indefinite J-nonnegative Sturm-Liouville operators, we present a criterion of similarity to a self-adjoint operator. This criterion is formulated in terms of Weyl-Titchmarsh m-functions. Moreover, using this result, we obtain a criterion, as well as simple sufficient conditions, formulated in terms of the coefficients of a given Sturm-Liouville operator.
This is a preview of subscription content, log in via an institution to check access.
References
R. V. Akopyan, Izv. Akad. Nauk Arm. SSR, Ser. Matem., 15:5 (1980), 357–364.
R. Beals, J. Differential Equations, 56:3 (1985), 391–407.
C. Bennewitz, Proc. London Math. Soc., (3), 59:2 (1989), 294–338.
P. Binding and A. Fleige, Oper. Matrices, 5:4 (2011), 735–755.
B. Ćurgus, A. Fleige, and A. Kostenko, Integral Equations Operator Theory, 77:4 (2013), 533–557.
B. Ćurgus and H. Langer, J. Differential Equations, 79:1 (1989), 31–61.
I. M. Karabash and A. S. Kostenko, Funkts. Anal. Prilozhen., 43:1 (2009), 81–84; English transl.: Functional Anal. Appl., 43:1 (2009), 65–68.
I. M. Karabash, A. S. Kostenko, and M. M. Malamud, J. Differential Equations, 246:3 (2009), 964–997.
I. M. Karabash and M. M. Malamud, Oper. Matrices, 1:3 (2007), 301–368.
J. Korevaar, Tauberian Theory: A Century of Developments, Springer-Verlag, Berlin, 2004.
A. Kostenko, Math. Nachr., (2014) (to appear), DOI: 10.1002/mana.201300104; http://arxiv.org/abs/1202.2444.
H. Langer, in: Lect. Notes in Math., vol. 948, 1982, 1–46.
I. S. Kac and M. G. Krein, “On the spectral function of the string,” Appendix II to F. Atkinson, Discrete and continuous boundary problems [in Russian], Mir, Moscow, 1968; English transl.: Amer. Math. Soc. Transl., Ser. 2, vol. 103, 1973, 19–102.
A. I. Parfyonov, Sibirsk. Mat. Zh., 44:4 (2003), 810–819; English transl.: Siberian Math. J., 44:4 (2003), 638–644.
S. G. Pyatkov, in: Nonclassical Equations of Mathematical Physics [in Russian], Izd-vo Inst. Matem. SO RAN, Novosibirsk, 2005, 240–251.
S. G. Pyatkov, in: Oper. Theory Adv. Appl., vol. 221, Birhäuser/Springer-Verlag, Basel, 2012, 549–570.
K. Veselić, Glasnik Math. Ser. III, 7:2 (1972), 229–248.
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 3, pp. 88–92, 2014
Original Russian Text Copyright © by A. S. Kostenko
The work is supported by the Austrian Science Fund (FWF), grant no. M1309-N13.
Rights and permissions
About this article
Cite this article
Kostenko, A.S. Spectral analysis of indefinite Sturm-Liouville operators. Funct Anal Its Appl 48, 227–230 (2014). https://doi.org/10.1007/s10688-014-0064-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10688-014-0064-x