Geodesic
On inverse problem for Sturm–Liouville operator with discontinuous coefficients
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 3-9 
E. N. Akhmedova; I. M. Huseynov. On inverse problem for Sturm–Liouville operator with discontinuous coefficients. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a0/
@article{ISU_2010_10_1_a0,
     author = {E. N. Akhmedova and I. M. Huseynov},
     title = {On inverse problem for {Sturm{\textendash}Liouville} operator with discontinuous coefficients},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {3--9},
     year = {2010},
     volume = {10},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a0/}
}
TY  - JOUR
AU  - E. N. Akhmedova
AU  - I. M. Huseynov
TI  - On inverse problem for Sturm–Liouville operator with discontinuous coefficients
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2010
SP  - 3
EP  - 9
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a0/
LA  - ru
ID  - ISU_2010_10_1_a0
ER  - 
%0 Journal Article
%A E. N. Akhmedova
%A I. M. Huseynov
%T On inverse problem for Sturm–Liouville operator with discontinuous coefficients
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2010
%P 3-9
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a0/
%G ru
%F ISU_2010_10_1_a0

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

In the paper uniqueness of reconstruction of the Sturm–Liouville operator with discontinuous coefficients by spectral data is proved and algorithm of construction of the potential is provided.

[1] Akhmedova E.N., “The definition of one class of Sturm–Liouville operators with discontinuous coefficients by Weyl function”, Proc. of IMM of NAS of Azerbaijan, XXII(XXX) (2005), 3–8 | MR | Zbl

[2] Gasymov M.G., “Pryamye i obratnye zadachi spektralnogo analiza dlya odnogo klassa uravnenii s razryvnymi koeffitsientami”, Neklassicheskie metody v geofizike, Materialy Mezhdunar. konf. (Novosibirsk), 1977, 37–44

[3] Guseinov I.M., Pashaev R.T., “Ob odnoi obratnoi zadache dlya differentsialnogo uravneniya vtorogo poryadka”, UMN, 57:3 (2002), 147–148 | DOI | MR | Zbl

[4] Yurko V.A., Vvedenie v teoriyu obratnykh spektralnykh zadach, M., 2007, 384 pp.

[5] Levitan B.M., Gasymov M.G., “Opredelenie differentsialnogo operatora po dvum spektram”, UMN, 19:2 (1964), 3–63 | MR | Zbl

[6] Marchenko V.A., Operatory Shturma–Liuvillya i ikh prilozheniya, Kiev, 1977, 331 pp. | MR

[7] Akhmedova E.N., “On representation of solution of Sturm–Liouville equation with discontinuous coefficients”, Proc. of IMM of NAS of Azerbaijan, XVI(XXIV) (2002), 5–9 | MR | Zbl

[8] Akhmedova E.N., Huseynov H.M., “On eigenvalues and eigenfunctions of one class of Sturm–Liouville operators with discontinuous coefficients”, Transactions of NAS of Azerbaijan, XXIII:4 (2003), 7–18 | MR | Zbl