Indefinite metrics,
Sturm–Liouville,
the Orr–Sommerfeld.
Subject:
The asymptotic behaviour of the spectrum of differential operators
Main publications:
S. N. Tumanov, A. A. Shkalikov, “O predelnom povedenii spektra modelnoi zadachi dlya uravneniya Orra–Zommerfelda s profilem Puazeilya”, Izv. RAN. Ser. matem, 66:4 (2002), 177–204
S. N. Tumanov, A. A. Shkalikov, “O lokalizatsii spektra zadachi Orra–Zommerfelda dlya bolshikh chisel Reinoldsa”, Matem. zametki, 72:4 (2002), 561–569
S. N. Tumanov, “Asimptoticheskie formuly dlya veschestvennykh sobstvennykh znachenii zadachi Shturma–Liuvillya s dvumya tochkami povorota”, Izv. RAN. Ser. matem., 65:5 (2001), 153–166
S. N. Tumanov, “Asimptotika sobstvennykh znachenii indefinitnoi zadachi Shturma–Liuvillya s dvumya tochkami povorota”, UMN, 55:5 (2000), 179–180
S. N. Tumanov, “Molchanov's criterion for compactness of the resolvent for a nonselfadjoint Sturm–Liouville operator”, Mat. Sb., 215:9 (2024), 125–146; Sb. Math., 215:9 (2024), 1249–1268
2023
2.
S. N. Tumanov, “On one condition for the discreteness of the spectrum and the compactness of the resolvent of a nonsectorial Sturm–Liouville operator on the semiaxis”, Dokl. RAN. Math. Inf. Proc. Upr., 510 (2023), 39–42; Dokl. Math., 107:2 (2023), 117–119
S. N. Tumanov, “A Completeness Theorem for the System of Eigenfunctions of the Complex Schrödinger Operator with Potential $q(x)=cx^\alpha$”, Mat. Zametki, 109:5 (2021), 797–800; Math. Notes, 109:5 (2021), 836–839
2002
4.
S. N. Tumanov, A. A. Shkalikov, “On the limit behaviour of the spectrum of a model problem for the Orr–Sommerfeld equation with Poiseuille profile”, Izv. RAN. Ser. Mat., 66:4 (2002), 177–204; Izv. Math., 66:4 (2002), 829–856
S. N. Tumanov, A. A. Shkalikov, “On the Spectrum Localization of the Orr–Sommerfeld Problem for Large Reynolds Numbers”, Mat. Zametki, 72:4 (2002), 561–569; Math. Notes, 72:4 (2002), 519–526
S. N. Tumanov, “Asymptotic formulae for the real eigenvalues of the Sturm–Liouville problem with two turning points”, Izv. RAN. Ser. Mat., 65:5 (2001), 153–166; Izv. Math., 65:5 (2001), 1003–1016
S. N. Tumanov, “Asymptotics of the eigenvalues of the indefinite Sturm–Liouville problem with two turning points”, Uspekhi Mat. Nauk, 55:5(335) (2000), 179–180; Russian Math. Surveys, 55:5 (2000), 1007–1008
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