The calculating of meanings of eigen functions of discrete semibounded from below operators via method of regularized traces
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2012), pp. 13-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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The numerical method of finding of meanings of eigenfunctions of discrete semibounded from below operator is developed. Estimates of residuals of sums of series of Reley–Schrodinger of the “weighed” corrections of the perturbation theory are gained. Approbation of the method on the example of Laplace operator with perturbed function of complex variable is produced.
Keywords: eigen values, eigen functions, “weighted”, corrections of perturbation theory, discrete operators.
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S. I. Kadchenko; S. N. Kakushkin. The calculating of meanings of eigen functions of discrete semibounded from below operators via method of regularized traces. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2012), pp. 13-21. http://geodesic.mathdoc.fr/item/VSGU_2012_6_a1/

[1] Sadovnichii V. A., Podolskii V. E., “Sledy operatorov”, Uspekhi matematicheskikh nauk, 61:5 (371) (2006), 89–156 | DOI | MR | Zbl

[2] Sviridyuk G. A., Bayazitova A. A., “O pryamoi i obratnoi zadachakh dlya uravnenii Khoffa na grafe”, Vestn. SamGTU. Ser.: Fiz.-mat. nauki, 2009, no. 1(18), 6–17

[3] Sviridyuk G. A., Zagrebina S. A., Pivovarova P. O., “Ustoichivost uravnenii Khoffa na grafe”, Vestn. SamGTU. Ser.: Fiz.-mat. nauki, 2010, no. 1(15), 6–15

[4] Sviridyuk G. A., Sukacheva T. G., “Bystro-medlennaya dinamika vyazkouprugikh sred”, DAN SSSR, 308:4 (1989), 791—794 | MR

[5] Sadovnichii V. A., Podolskii V. E., “O vychislenii pervykh sobstvennykh znachenii operatora Shturma–Liuvillya”, DAN, 346:2 (1996), 162–164 | MR

[6] Kadchenko S. I., “Novyi metod vychisleniya sobstvennykh chisel spektralnoi zadachi Orra–Zommerfelda”, Elektromagnitnye volny i elektronnye sistemy, 5:6 (2000), 4–10 | MR

[7] Kadchenko S. I., Ryazanova L. S., “Chislennyi metod nakhozhdeniya sobstvennykh znachenii diskretnykh poluogranichennykh snizu operatorov”, Vestnik YuUrGU. Ser.: Matematicheskoe modelirovanie i programmirovanie. Vyp. 8, 2011, no. 17(234), 46–51 | Zbl

[8] Sadovnichii V. A., Teoriya operatorov, Ucheb. dlya vuzov s uglublennym izucheniem matematiki, 5-e izd., stereotip., Drofa, M., 2004, 384 pp.

[9] Sadovnichii V. A., Dubrovskii V. V., “Zamechanie ob odnom novom metode vychisleniya sobstvennykh znachenii i sobstvennykh funktsii diskretnykh operatorov”, Tr. seminara I. G. Petrovskogo, 17, Izd-vo MGU, M., 1994, 244–248 | MR

[10] Dubrovskii V. V., Sedov A. I., “Otsenka raznosti spektralnykh funktsii operatorov tipa Lezhandra”, Fundamentalnaya i prikladnaya matematika, 6:4 (2000), 1075–1082 | MR

[11] Dubrovskii V. V., Sedov A. I., “Otsenka raznosti spektralnykh funktsii operatorov tipa Gegenbauera po norme $L_q$”, Izvestiya vysshikh uchebnykh zavedenii. Ser.: Matematika, 1999, no. 8(447), 20–25 | MR

[12] Dubrovskii V. V., Sedov A. I., “Otsenka raznosti spektralnykh funktsii samosopryazhennykh operatorov”, Elektromagnitnye volny i elektronnye sistemy, 5:5 (2000), 10–13 | MR

[13] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 528 pp. | MR