Geodesic
On the spectrum and bases of eigenfunctions of a problem connected with oscillations of a rotating fluid
Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 219-226 
S. A. Gabov. On the spectrum and bases of eigenfunctions of a problem connected with oscillations of a rotating fluid. Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/SM_1983_44_2_a5/
@article{SM_1983_44_2_a5,
     author = {S. A. Gabov},
     title = {On the spectrum and bases of eigenfunctions of a~problem connected with oscillations of a~rotating fluid},
     journal = {Sbornik. Mathematics},
     pages = {219--226},
     year = {1983},
     volume = {44},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_2_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author considers the eigenvalue problem \begin{gather*} \Delta u-\mu^2\,\frac{\lambda^2-k^2}{\lambda^2-\beta^2}\,u=0,\qquad x\in D\subset\mathbf R^2, \\ \frac{\partial u}{\partial n}+i\,\frac k\lambda\,\frac{\partial u}{\partial \tau}=0, \qquad x\in\partial D, \end{gather*} which arises in studying the problem of normal oscillations of a rotating exponentially stratified liquid in a cylindrical container. It is shown that the spectrum is real and localized in the neighborhood of two limit points $\lambda=\pm\beta$, and the system of eigenvalues forms a two-fold Riesz basis in $L_2(D)$. Bibliography: 9 titles.

[1] Sretenskii L. N., Teoriya volnovykh dvizhenii zhidkosti, ONTI NKTP, M., L., 1936

[2] Sobolev S. L., “Ob odnoi novoi zadache matematicheskoi fiziki”, Izv. AN SSSR, ser. matem., 18 (1954), 3–50 | MR | Zbl

[3] Gabov S. A., “O polnote i bazisnosti sistemy sobstvennykh funktsii odnoi zadachi, voznikayuschei v teorii prilivnykh kolebanii”, DAN SSSR, 250:4 (1980), 780–782 | MR | Zbl

[4] Gabov S. A., “O spektre odnoi zadachi S. L. Soboleva”, DAN SSSR, 253:3 (1980), 521–524 | MR | Zbl

[5] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977

[6] Gabov S. A., “Uglovoi potentsial i ego nekotorye prilozheniya”, Matem. sb., 103(145) (1977), 490–504 | MR | Zbl

[7] Gabov S. A., “Funktsiya Grina operatora Laplasa v ploskoi zadache s kosoi proizvodnoi s postoyannymi koeffitsientami”, ZhVM, 18:3 (1978), 660–671 | MR | Zbl

[8] Gyunter N. M., Teoriya potentsiala i ee primeneniya k osnovnym zadacham matematicheskoi fiziki, Gostekhizdat, M., 1953 | MR

[9] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965