Geodesic
Spectral analysis of a~fourth order differential operator with periodic and antiperiodic boundary conditions
Algebra i analiz, Tome 27 (2015) no. 5, pp. 117-152.

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}
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D. M. Polyakov. Spectral analysis of a~fourth order differential operator with periodic and antiperiodic boundary conditions. Algebra i analiz, Tome 27 (2015) no. 5, pp. 117-152. http://geodesic.mathdoc.fr/item/AA_2015_27_5_a4/

[1] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR

[2] Kollatts L., Zadachi na sobstvennye znacheniya s tekhnicheskimi prilozheniyami, Nauka, M., 1968

[3] Yakubovich V. A., Starzhinskii V. M., Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya, Nauka, M., 1972 | MR

[4] Korotyaev E., Lobanov I., “Schrödinger operators on zigzag nanotubes”, Ann. Henri Poincare, 8:6 (2007), 1151–1176 | DOI | MR | Zbl

[5] Badanin A., Korotyaev E., “Spectral asymptotics for periodic fourth-order operators”, Int. Math. Res. Not. IMRN, 2005:45 (2005), 2775–2814 | DOI | MR | Zbl

[6] Badanin A. V., Korotyaev E. L., “Spektralnye otsenki dlya periodicheskogo operatora chetvertogo poryadka”, Algebra i analiz, 22:5 (2010), 1–48 | MR | Zbl

[7] Badanin A., Korotyaev E., Eigenvalue asymptotics for fourth order operators on the unit interval, arXiv: 1309.3449

[8] Badanin A., Korotyaev E., “Even order periodic operators on the real line”, Int. Math. Res. Not. IMRN, 2012:5 (2012), 1143–1194 | MR | Zbl

[9] Veliev O. A., “On the nonself-adjoint ordinary differential operators with periodic boundary conditions”, Israel J. Math., 176 (2010), 195–207 | DOI | MR | Zbl

[10] Mikhailets V., Molyboga V., “Singular eigenvalue problems on the circle”, Methods Funct. Anal. Topology, 10:3 (2004), 44–53 | MR | Zbl

[11] Mikhailets V., Molyboga V., “Uniform estimates for the semi-periodic eigenvalues of the singular differential operators”, Methods Funct. Anal. Topology, 10:4 (2004), 30–57 | MR | Zbl

[12] Molyboga V., “Estimates for periodic eigenvalues of the differential operator $(-1)^md^{2m}/dx^{2m}+V$ with $V$-distribution”, Methods Funct. Anal. Topology, 9:2 (2003), 163–178 | MR | Zbl

[13] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[14] Dzhakov P., Mityagin B. S., “Zony neustoichivosti odnomernykh periodicheskikh operatorov Shrëdingera i Diraka”, Uspekhi mat. nauk, 61:4 (2006), 77–182 | DOI | MR | Zbl

[15] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[16] Danford N., Shvarts Dzh. T., Lineinye operatory. Spektralnye operatory, v. III, Mir, M., 1974

[17] Agranovich M. S., “Spektralnye svoistva zadach difraktsii”: Voitovich N. N., Katselembaum B. Z., Sivov A. N., Obobschennyi metod sobstvennykh kolebanii v teorii difraktsii, Nauka, M., 1977, 289–416 | MR

[18] Baskakov A. G., “Metody abstraktnogo garmonicheskogo analiza v teorii vozmuschenii lineinykh operatorov”, Sib. mat. zh., 24:1 (1983), 21–39 | MR | Zbl | Zbl

[19] Baskakov A. G., “Metod usredneniya v teorii vozmuschenii lineinykh differentsialnykh operatorov”, Differents. uravneniya, 21:4 (1985), 555–562 | MR | Zbl

[20] Baskakov A. G., “Teoriya o rasscheplenii operatora i nekotorye smezhnye voprosy analiticheskoi teorii vozmuschenii”, Izv. AN SSSR. Ser. mat., 50:3 (1986), 435–457 | MR | Zbl

[21] Baskakov A. G., “Spektralnyi analiz vozmuschennykh nekvazianaliticheskikh i spektralnykh operatorov”, Izv. RAN. Cer. mat., 58:4 (1994), 3–32 | MR | Zbl

[22] Baskakov A. G., Derbushev A. V., Scherbakov A. O., “Metod podobnykh operatorov v spektralnom analize nesamosopryazhennogo operatora Diraka s negladkim potentsialom”, Izv. RAN. Ser. mat., 75:3 (2011), 3–28 | DOI | MR | Zbl

[23] Polyakov D. M., “Spektralnyi analiz nesamosopryazhennogo operatora chetvertogo poryadka s negladkimi koeffitsientami”, Sib. mat. zh., 56:1 (2015), 165–184 | Zbl

[24] Polyakov D. M., “Spektralnye svoistva differentsialnogo operatora chetvertogo poryadka”, Vestnik VGU. Ser. fiz. mat., 2012, no. 1, 179–181 | Zbl

[25] Polyakov D. M., “O spektralnykh svoistvakh differentsialnogo operatora chetvertogo poryadka s periodicheskimi i antiperiodicheskimi kraevymi usloviyami”, Izv. vuzov. Mat., 2015, no. 5, 75–79 | Zbl

[26] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR

[27] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR

[28] Khenri D., Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985 | MR

[29] Engel K.-J., Nagel R., One-parameter semigroups for linear evolution equations, Grad. Texts in Math., 194, Springer-Verlag, New York, 2000 | MR | Zbl