Geodesic
Spectra of discrete symplectic eigenvalue problems with separated boundary conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2011), pp. 84-88

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In this paper we consider a discrete symplectic eigenvalue problem with separated boundary conditions and obtain formulas for the number of eigenvalues on a given interval of the variation of the spectral parameter. In addition, we compare the spectra of two symplectic eigenvalue problems with different separated boundary conditions.
Keywords: discrete symplectic eigenvalue problems, relative oscillation theory, comparative index. 
Yu. V. Eliseeva. Spectra of discrete symplectic eigenvalue problems with separated boundary conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2011), pp. 84-88. http://geodesic.mathdoc.fr/item/IVM_2011_11_a9/
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[1] Gokhberg I. Ts., Krein M. G., Teoriya volterrovykh operatorov v gilbertovom prostranstve, Nauka, M., 1967

[2] Atkinson F., Diskretnye i nepreryvnye granichnye zadachi, Mir, M., 1968 | MR | Zbl

[3] Kratz W., Quadratic functionals in variational analysis and control theory, Akademie Verlag, Berlin, 1995 | MR | Zbl

[4] Bohner M., Došlý O., Kratz W., “An oscillation theorem for discrete eigenvalue problems”, Rocky Mountain J. Math., 33:4 (2003), 1233–1260 | DOI | MR | Zbl

[5] Došlý O., Kratz W., “Oscillation theorems for symplectic difference systems”, J. Difference Equ. Appl., 13:7 (2007), 585–605 | DOI | MR

[6] Došlý O., Kratz W., “Oscillation and spectral theory for symplectic difference systems with separated boundary conditions”, J. Difference Equ. Appl., 16:7 (2010), 831–846 | DOI | MR

[7] Bohner M., Došlý O., “Disconjugacy and transformations for symplectic systems”, Rocky Mountain J. Math., 27:3 (1997), 707–743 | DOI | MR | Zbl

[8] Kratz W., “Discrete oscillation”, J. Difference Equ. Appl., 9:1 (2003), 135–147 | MR | Zbl

[9] Ammann K., Teschl G., “Relative oscillation theory for Jacobi matrices”, Proc. 14th Intern. Conf. on Difference Equations and Applications, ed. M. Bohner et al., Uğur-Bahçeşehir University Publishing Co, Istanbul, 2009, 105–115 | MR

[10] Krüger H., Teschl G., “Relative oscillation theory, weighted zeros of the wronskian, and spectral shift function”, Commun. Math. Phys., 287:2 (2009), 613–640 | DOI | MR

[11] Teschl G., “Oscillation theory and renormalized oscillation theory for Jacobi operators”, J. Diff. Equ., 129:2 (1996), 532–558 | DOI | MR | Zbl

[12] Eliseeva Yu.V., “Teoremy sravneniya dlya simplekticheskikh sistem raznostnykh uravnenii”, Differents. uravneniya, 46:9 (2010), 1329–1342 | MR | Zbl

[13] Elyseeva J., “On relative oscillation theory for symplectic eigenvalue problems”, Appl. Math. Lett., 23:10 (2010), 1231–1237 | DOI | MR | Zbl

[14] Eliseeva Yu. V., “Sravnitelnyi indeks dlya reshenii simplekticheskikh sistem raznostnykh uravnenii”, Differents. uravneniya, 45:3 (2009), 431–444 | MR | Zbl

[15] Gantmakher F. R., Teoriya matrits, Fizmatlit, M., 2004

[16] Golub Dzh., Van Loun Ch., Matrichnye vychisleniya, Mir, M., 1999