Geodesic
Spectral Analysis of Indefinite Sturm--Liouville Operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 88-92.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Sturm–Liouville operator, $J$-nonnegative operator, critical point, similarity to a self-adjoint operator. 
@article{FAA_2014_48_3_a7,
     author = {A. S. Kostenko},
     title = {Spectral {Analysis} of {Indefinite} {Sturm--Liouville} {Operators}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {88--92},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a7/}
}
TY  - JOUR
AU  - A. S. Kostenko
TI  - Spectral Analysis of Indefinite Sturm--Liouville Operators
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2014
SP  - 88
EP  - 92
VL  - 48
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a7/
LA  - ru
ID  - FAA_2014_48_3_a7
ER  - 
%0 Journal Article
%A A. S. Kostenko
%T Spectral Analysis of Indefinite Sturm--Liouville Operators
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2014
%P 88-92
%V 48
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a7/
%G ru
%F FAA_2014_48_3_a7
A. S. Kostenko. Spectral Analysis of Indefinite Sturm--Liouville Operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 88-92. http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a7/

[1] R. V. Akopyan, Izv. AN Arm. SSR, Ser. matem., 15:5 (1980), 357–364 | MR | Zbl

[2] R. Beals, J. Differential Equations, 56:3 (1985), 391–407 | DOI | MR | Zbl

[3] C. Bennewitz, Proc. London Math. Soc., (3), 59:2 (1989), 294–338 | DOI | MR | Zbl

[4] P. Binding, A. Fleige, Oper. Matrices, 5:4 (2011), 735–755 | DOI | MR | Zbl

[5] B. Ćurgus, A. Fleige, A. Kostenko, Integral Equations Operator Theory, 77:4 (2013), 533–557 | DOI | MR | Zbl

[6] B. Ćurgus, H. Langer, J. Differential Equations, 79:1 (1989), 31–61 | DOI | MR | Zbl

[7] I. M. Karabash, A. S. Kostenko, Funkts. analiz i ego pril., 43:1 (2009), 81–84 | DOI | MR | Zbl

[8] I. M. Karabash, A. S. Kostenko, M. M. Malamud, J. Differential Equations, 246:3 (2009), 964–997 | DOI | MR | Zbl

[9] I. M. Karabash, M. M. Malamud, Oper. Matrices, 1:3 (2007), 301–368 | DOI | MR | Zbl

[10] J. Korevaar, Tauberian Theory: A Century of Developments, Springer-Verlag, Berlin, 2004 | MR | Zbl

[11] A. Kostenko, Math. Nachr., 2014 (to appear) , arXiv: 1202.2444 | DOI

[12] H. Langer, Lect. Notes in Math., 948 (1982), 1–46 | DOI | MR | Zbl

[13] I. S. Kats, M. G. Krein, “O spektralnykh funktsiyakh struny”, Dop. II k knige: F. Atkinson, Diskretnye i nepreryvnye zadachi, Mir, M., 1968 | MR

[14] A. I. Parfenov, Sib. matem. zhurn., 44:4 (2003), 810–819 | MR | Zbl

[15] S. G. Pyatkov, Neklassicheskie uravneniya matematicheskoi fiziki, Izd-vo Instituta matematiki SO RAN, Novosibirsk, 2005, 240–251 | Zbl

[16] S. G. Pyatkov, Oper. Theory Adv. Appl., 221 (2012), 549–570, Birhäuser/Springer-Verlag, Basel | MR

[17] K. Veselić, Glasnik Math. Ser. III, 7:2 (1972), 229–248 | MR | Zbl