Spectral properties of the singular ordinary differential operators are investigated. Are calculated the regularizated traces of the perturbated singular ordinary differential operators, is found asimptotic of eigenvalues, return problems are decided.
Biography
Graduated from Faculty of Mathematics and Physics of Magnitogorsk State Pedagogical Institute (MSPI). Ph. D. thesis was defended in 2000. A list of my works contains more than 20 titles.
Main publications:
Dubrovskii V. V., Sedov A. I. Asimptotika sobstvennykh znachenii singulyarnogo differentsialnogo operatora tipa Yakobi // Dokl. RAN, 1997, 353(3), 295–299.
Dubrovskii V. V., Sedov A. I. Otsenka raznosti spektralnykh funktsii operatorov tipa Gegenbauera po norme $L_q$ // Izv. vuzov, ser. matem., 1999, 447(8), 20–25.
Dubrovskii V. V., Sedov A. I. Otsenka raznosti spektralnykh funktsii samosopryazhennykh operatorov // Elektromagnitnye volny i elektronnye sistemy, 2000, 5(5), 10–13.
Sadovnichii V. A., Dubrovskii V. V., Sedov A. I., Tipko A. N. Obratnaya zadacha spektralnogo analiza dlya operatora Yakobi s potentsialom // Dokl. RAN, 2001, 381(3), 313–314.
A. I. Sedov, “Prediction of multidimensional time series by method of inverse spectral problem”, J. Comp. Eng. Math., 9:1 (2022), 35–42
2.
A. I. Sedov, “Determining of continuous delay in a spectral problem for Chebyshev operator of the first kind”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 14:4 (2022), 34–39
2019
3.
A. I. Sedov, “The use of the inverse problem of spectral analysis to forecast time series”, J. Comp. Eng. Math., 6:1 (2019), 74–78
A. I. Sedov, “On calculation of eigenvalues and eigenfunctions of a discrete operator with a nuclear resolvent perturbed by a bounded operator”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 11:1 (2019), 16–23
A. I. Sedov, “About the approximate solution of the inverse problem of the spectral analysis for Laplace operator”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2010, no. 5, 73–78
A. I. Sedov, G. A. Zakirova, “The inverse spectral problem for a power of the Laplace operator in the case of the Neuman problem on a parallelepiped”, Vestnik Chelyabinsk. Gos. Univ., 2008, no. 10, 63–67
2000
8.
V. V. Dubrovskii, A. I. Sedov, “Estimation of the difference of spectral functions of the Legendre-type operators”, Fundam. Prikl. Mat., 6:4 (2000), 1075–1082
V. V. Dubrovskii, A. I. Sedov, “An estimate for the difference of spectral functions of Gegenbauer-type operators in the norm of $L_q$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 8, 20–25; Russian Math. (Iz. VUZ), 43:8 (1999), 17–22
V. V. Dubrovskii, A. I. Sedov, “Asymptotics of the eigenvalues of a singular differential operator
of Jacobi type”, Dokl. Akad. Nauk, 353:3 (1997), 295–299
A. I. Sedov, “The asymptotics for eigenvalues of a differential Jacobi-type operator with $\alpha=\frac{1}{2}$ and $\beta=-\frac{1}{2}$”, Fundam. Prikl. Mat., 2:1 (1996), 309–312
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