Geodesic
Partially-isospectral Sturm--Liouville boundary value problems on the finite segment
Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 104-113.

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

In paper, an algorithm is proposed for constructing isospectral and partially-isospectral Sturm–Liouville boundary value problems on the finite segment.
Keywords: Sturm–Liouville problem, eigenvalues, normalizing constants, spectral data, inverse spectral problem, integral equation, partially-isospectral operators. 
@article{CHEB_2023_24_1_a7,
     author = {O. E. Mirzaev},
     title = {Partially-isospectral {Sturm--Liouville} boundary value problems on the finite segment},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {104--113},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a7/}
}
TY  - JOUR
AU  - O. E. Mirzaev
TI  - Partially-isospectral Sturm--Liouville boundary value problems on the finite segment
JO  - Čebyševskij sbornik
PY  - 2023
SP  - 104
EP  - 113
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a7/
LA  - ru
ID  - CHEB_2023_24_1_a7
ER  - 
%0 Journal Article
%A O. E. Mirzaev
%T Partially-isospectral Sturm--Liouville boundary value problems on the finite segment
%J Čebyševskij sbornik
%D 2023
%P 104-113
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a7/
%G ru
%F CHEB_2023_24_1_a7
O. E. Mirzaev. Partially-isospectral Sturm--Liouville boundary value problems on the finite segment. Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 104-113. http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a7/

[1] Marchenko V. A., “Some problems in the theory of one-dimensional linear differential operators of the second order I”, Tr. MMO, 1, GITTL, M.-L., 1952, 327–420

[2] Gelfand I. M., Levitan B. M., “On the determination of a differential equation from its spectral function”, Izv. Academy of Sciences of the USSR. Ser. math., 15:4 (1951), 309–360 | Zbl

[3] Levitan B. M., Sargsyan I. S., Sturm–Liouville and Dirac operators, Kluwer Acad. Publ., Dordrecht, 1990 | MR | MR | Zbl

[4] Isaacson E. L., Trubowitz E., “The inverse Sturm–Liouville problem I”, Comm. Pure Appl. Math., 36 (1983), 767–783 | DOI | MR | Zbl

[5] Isaacson E. L., McKean H. P., Trubowitz E., “The inverse Sturm–Liouville problem II”, Comm. Pure Appl. Math., 37 (1984), 1–11 | DOI | MR | Zbl

[6] Dahlberg B. E., Trubowitz E., “The inverse Sturm–Liouville problem III”, Comm. Pure Appl. Math., 37 (1984), 255–267 | DOI | MR | Zbl

[7] Poschel J., Trubowitz E., Inverse spectral theory, Academic Press, New York, 1987 | MR | Zbl

[8] Savchuk A. M., Shkalikov A. A., “On the properties of maps connected with inverse Sturm–Liouville problems”, Proc. Steklov Inst. Math., 260 (2008), 218–237 | DOI | MR | Zbl

[9] Yurko V. A., Introduction into the theory of inverse spectral problems, Fizmatlit, M., 2007

[10] Jodeit M., Levitan B. M., “The isospectrality problem for the classical Sturm–Liouville equation”, Advances in differential equations, 2:2 (1997), 297–318 | DOI | MR | Zbl

[11] Ashrafyan Y. A., Harutyunyan T. N., “Inverse Sturm–Liouville problems with fixed boundary conditions”, Electronic Journal of differential equations, 2015:27 (2015), 1–8 | MR

[12] Alimov Sh. A., “The work of A. N. Tikhonov on inverse problems for the Sturm–Liouville equation”, Russian Math. Surveys, 31:6 (1976), 87–92 | DOI | MR | Zbl | Zbl

[13] Ambartsumyan V. A., “Über eine Frage Eigenwerttheorie”, Zeitschr. für Physik, 53 (1929), 690–695 | DOI

[14] Mirzaev O. E., Khasanov A. B., “On families of isospectral Sturm–Liouville boundary value problems”, Ufa Mathematical Journal, 12:2 (2020), 28–34 | MR | Zbl

[15] Mirzaev O. E., Murodov F. M., “Isospectral Sturm–Liouville operators on the finite segment”, Scientific Journal Samarkand State University, 2020, no. 3(121), 50–55

[16] Mirzaev O. E., “Isospectral Sturm–Liouville operators on the finite segment”, Scientific Journal Samarkand State University, 2020, no. 5(123), 60–64

[17] Namig J. Guliyev, “Essentially isospectral transformations and their applications”, Annali di Matematica Pura ed Applicata (1923-), 199 (2020), 1621–1648 | DOI | MR | Zbl