Computation of eigenvalues of perturbed discrete semibounded operators. (Russian. English summary) Zbl 07811639
Zh. Vychisl. Mat. Mat. Fiz. 46, No. 7, 1265-1272 (2006); translation in Comput. Math. Math. Phys. 46, No. 7, 1200-1206 (2006).
Summary: To compute the eigenvalues of a perturbed discrete semibounded operator, systems are obtained for the first time in which the number of equations is equal to the multiplicity of the corresponding eigenvalues of the unperturbed operator.
MSC:
| 47J10 | Nonlinear spectral theory, nonlinear eigenvalue problems |
Keywords:
separable Hilbert space; discrete operator; eigenvalues and eigenfunctions of operator; multiplicity of eigenvalue; perturbative correctionsReferences:
| [1] | Sadovnichii V. A., Dubrovskii V. V., “Zamechanie ob odnom novom metode vychisleniya sobstvennykh znachenii i sobstvennykh funktsii diskretnykh operatorov”, Tr. seminara im. I. G. Petrovskogo, 17, MGU, M., 1994, 244-248 |
| [2] | Sadovnichii V. A., Podolskii V. E., “O vychislenii pervykh sobstvennykh znachenii operatora Shturma-Liuvillya”, Dokl. RAN, 346:2 (1996), 162-164 |
| [3] | Dorodnitsyn A. A., “Asimptoticheskie zakony raspredeleniya sobstvennykh znachenii dlya nekotorykh vidov differentsialnykh uravnenii vtorogo poryadka”, Uspekhi matem. nauk, 7:6 (1952), 3-96 · Zbl 0048.32402 |
| [4] | Dikii L. A., “Novyi sposob priblizhennogo vychisleniya sobstvennykh chisel zadachi Shturma-Liuvillya”, Dokl. AN SSSR, 116:1 (1957), 12-14 · Zbl 0091.29203 |
| [5] | Dikii L. A., “Formuly dlya differentsialnykh operatorov Shturma-Liuvillya”, Uspekhi matem. nauk, 13:3 (1958), 111-143 · Zbl 0080.06703 |
| [6] | Shkarin S. A., “O sposobe Gelfanda-Dikogo vychisleniya pervykh sobstvennykh chisel operatora Shturma-Liuvillya”, Vestn. MGU. Ser. 1. Matem., mekhan., 1996, no. 1, 39-44 · Zbl 0881.47012 |
| [7] | Kadchenko S. I., Novyi metod vychisleniya sobstvennykh chisel vozmuschennykh samosopryazhennykh operatorov, Dis. \( \dots\) dokt. fiz.-matem. nauk, MaGU, Magnitogorsk, 2004 |
| [8] | Sadovnichii V. A., Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., “Vychislenie pervykh sobstvennykh chisel kraevoi zadachi gidrodinamicheskoi ustoichivosti techeniya mezhdu parallelnymi ploskostyami pri malykh chislakh Reinoldsa”, Dokl. RAN, 335:5 (1997), 600-604 |
| [9] | Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A., “Novyi metod priblizhennogo vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi Orra-Zommerfelda”, Dokl. RAN, 378:4 (2001), 443-446 |
| [10] | Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A., “Novyi metod priblizhennogo vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi gidrodinamicheskoi ustoichivosti techeniya Puazeilya v krugloi trube”, Dokl. RAN, 380:2 (2001), 160-163 |
| [11] | Sadovnichii V. A., Teoriya operatorov, Vyssh. shkola, M., 1999 |
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