Geodesic
A Sturm--Liouville Inverse Spectral Problem with Boundary Conditions Depending on the Spectral Parameter
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 74-77.

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

We consider a boundary value problem generated by the Sturm-Liouville equation on a finite interval. Both the equation and the boundary conditions depend quadratically on the spectral parameter. This boundary value problem occurs in the theory of small vibrations of a damped string. The inverse problem, i.e., the problem of recovering the equation and the boundary conditions from the given spectrum, is solved.
Mots-clés : Sturm–Liouville problem
Keywords: damped string, spectral parameter-dependent boundary conditions, eigenvalues, asymptotics. 
@article{FAA_2002_36_4_a7,
     author = {C. Van der Mee and V. N. Pyvovarchyk},
     title = {A {Sturm--Liouville} {Inverse} {Spectral} {Problem} with {Boundary} {Conditions} {Depending} on the {Spectral} {Parameter}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {74--77},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a7/}
}
TY  - JOUR
AU  - C. Van der Mee
AU  - V. N. Pyvovarchyk
TI  - A Sturm--Liouville Inverse Spectral Problem with Boundary Conditions Depending on the Spectral Parameter
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2002
SP  - 74
EP  - 77
VL  - 36
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a7/
LA  - ru
ID  - FAA_2002_36_4_a7
ER  - 
%0 Journal Article
%A C. Van der Mee
%A V. N. Pyvovarchyk
%T A Sturm--Liouville Inverse Spectral Problem with Boundary Conditions Depending on the Spectral Parameter
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2002
%P 74-77
%V 36
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a7/
%G ru
%F FAA_2002_36_4_a7
C. Van der Mee; V. N. Pyvovarchyk. A Sturm--Liouville Inverse Spectral Problem with Boundary Conditions Depending on the Spectral Parameter. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 74-77. http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a7/

[1] Pivovarchik V. N., “Direct and inverse problems for a damped string”, J. Operator Theory, 42 (1999), 189–220 | MR | Zbl

[2] Kurant R., Gilbert D., Metody matematicheskoi fiziki, t. I, Gostekhizdat, M., 1951 | MR

[3] Krein M. G., Langer G., Trudy mezhdunarodnogo simpoziuma po prilozheniyam teorii funktsii v mekhanike sploshnoi sredy, T. 2, Nauka, M., 1965, 283–322 ; Krein M. G., Langer H., Integral Equations and Operator Theory, 1:4 (1978), 539–566 | MR | DOI | MR | Zbl

[4] Van der Mee C., Pivovarchik V. N., “The inverse generalized Regge problem”, Inverse Problems, 17 (2001), 1831–1845 | DOI | MR | Zbl

[5] Marchenko V. A., Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova Dumka, Kiev, 1977 | MR

[6] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GTIZ, M., 1956

[7] Levin B. Ya., Ostrovskii I. V., “O malykh vozmuscheniyakh mnozhestva kornei funktsii tipa sinusa”, Izv. AN SSSR, ser. matem., 43:1 (1979), 87–110 | MR