Geodesic
On inverse Sturm--Liouville problems on a finite segment
Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 923-934.

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

A necessary and sufficient condition for reconstructing the differential operator $-y''+dF\cdot y$, where $F$ is a function of bounded variation, from the spectra of two boundary value problems on the segment $[0,\pi]$, is established in this paper. 
@article{IM2_1967_1_5_a1,
     author = {V. V. Zhikov},
     title = {On inverse {Sturm--Liouville} problems on a finite segment},
     journal = {Izvestiya. Mathematics },
     pages = {923--934},
     publisher = {mathdoc},
     volume = {1},
     number = {5},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a1/}
}
TY  - JOUR
AU  - V. V. Zhikov
TI  - On inverse Sturm--Liouville problems on a finite segment
JO  - Izvestiya. Mathematics 
PY  - 1967
SP  - 923
EP  - 934
VL  - 1
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a1/
LA  - en
ID  - IM2_1967_1_5_a1
ER  - 
%0 Journal Article
%A V. V. Zhikov
%T On inverse Sturm--Liouville problems on a finite segment
%J Izvestiya. Mathematics 
%D 1967
%P 923-934
%V 1
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a1/
%G en
%F IM2_1967_1_5_a1
V. V. Zhikov. On inverse Sturm--Liouville problems on a finite segment. Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 923-934. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a1/

[1] Gelfand I. M., Levitan B. M., “Ob opredelenii differentsialnogo uravneniya po ego spektralnoi funktsii”, Izv. AN SSSR. Ser. matem., 15 (1951), 309–360 | MR | Zbl

[2] Krein M. G., “Opredelenie plotnosti neodnorodnoi simmetrichnoi struny po spektru ee chastot”, Dokl. AN SSSR, 76:3 (1951), 345–348 | MR | Zbl

[3] Levitan B. M., “Ob opredelenii differentsialnogo uravneniya Shturma–Liuvillya po dvum spektram”, Dokl. AN SSSR, 150:3 (1963), 474–476 | MR | Zbl

[4] Marchenko V. A., “Razlozhenie po sobstvennym funktsiyam nesamosopryazhennykh operatorov vtorogo poryadka”, Matem. sb., 52:2 (1960), 739–788

[5] Levitan B. M., “Asimptoticheskoe povedenie spektralnoi funktsii samosopryazhennogo differentsialnogo uravneniya vtorogo poryadka”, Izv. AN SSSR. Ser. matem., 17 (1953), 331–364 | MR | Zbl

[6] Levitan B. M., Razlozheniya po sobstvennym funktsiyam, Fizmatgiz, M., 1953

[7] Akhiezer N., Krein M., O nekotorykh voprosakh teorii momentov, GONTI, Kharkov, 1938

[8] Gasymov M. G., Levitan B. M., “O differentsialnykh operatorakh Shturma–Liuvillya”, Matem. sb., 63(105):3 (1964), 445–458 | MR | Zbl

[9] Levitan B. M., Gasymov M. G., “Opredelenie differentsialnogo uravneniya po dvum spektram”, Uspekhi matem. nauk, 19:2 (1964), 3–63 | MR | Zbl

[10] Krein M. G., “O perekhodnoi funktsii odnomernoi kraevoi zadachi vtorogo poryadka”, Dokl. AN SSSR, 88:3 (1953), 405–408 | MR | Zbl