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Filonov, Nikolai Dmitrievich
Statistics Math-Net.Ru
Total publications: 27
Scientific articles: 27
Presentations: 5

Number of views:
This page:2387
Abstract pages:9119
Full texts:2604
References:1100
Associate professor
Candidate of physico-mathematical sciences
E-mail: ,

https://www.mathnet.ru/eng/person37236
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/609754

Publications in Math-Net.Ru Citations
2023
1. N. D. Filonov, “On the set of values of a ternary quadratic form”, Algebra i Analiz, 35:4 (2023),  183–193  mathnet
2022
2. S. T. Krymskiĭ, N. D. Filonov, “On the rate of decrease at infinity of solutions to the Schrödinger equation in a half-cylinder”, Algebra i Analiz, 34:1 (2022),  105–122  mathnet  mathscinet; St. Petersburg Math. J., 34:1 (2023), 79–92 1
2021
3. N. D. Filonov, “Absence of the eigenvalues in the spectra of operators with partially periodic coefficients”, Algebra i Analiz, 33:5 (2021),  176–192  mathnet; St. Petersburg Math. J., 33:5 (2022), 867–878
4. N. D. Filonov, “Schrödinger operator in a cylinder with a decreasing potential”, Algebra i Analiz, 33:1 (2021),  213–245  mathnet; St. Petersburg Math. J., 33:1 (2022), 155–178 1
5. N. D. Filonov, P. A. Hodunov, “On the local boundedness of solutions to the equation $-\Delta u+a\partial_zu=0$”, Zap. Nauchn. Sem. POMI, 508 (2021),  173–184  mathnet 1
2020
6. N. Filonov, P. A. Khodunov, “Nonuniqueness of Leray-Hopf solutions for a dyadic model”, Algebra i Analiz, 32:2 (2020),  229–253  mathnet  elib; St. Petersburg Math. J., 32:2 (2021), 371–387  isi  scopus 3
7. N. D. Filonov, “Maxwell operator in a cylinder with coefficients that do not depend on the cross-sectional variables”, Algebra i Analiz, 32:1 (2020),  187–207  mathnet  elib; St. Petersburg Math. J., 32:1 (2021), 139–154  isi  scopus 1
8. I. Kachkovskii, N. D. Filonov, “Absolute continuity of the spectrum of the periodic Schrödinger operator in a cylinder with Robin boundary condition”, Funktsional. Anal. i Prilozhen., 54:2 (2020),  48–57  mathnet  mathscinet 1
2018
9. N. Filonov, “Maxwell operator in a cylinder with coefficients that do not depend on the longitudinal variable”, Algebra i Analiz, 30:3 (2018),  210–249  mathnet  mathscinet  elib; St. Petersburg Math. J., 30:3 (2019), 545–572  isi  scopus 1
10. N. D. Filonov, “Number of non-zero cubic sums”, Zap. Nauchn. Sem. POMI, 469 (2018),  160–174  mathnet; J. Math. Sci. (N. Y.), 242:4 (2019), 575–585  scopus 1
2017
11. A. O. Prokhorov, N. D. Filonov, “The Maxwell operator with periodic coefficients in a cylinder”, Algebra i Analiz, 29:6 (2017),  182–196  mathnet  mathscinet  elib; St. Petersburg Math. J., 29:6 (2018), 997–1006  isi 4
12. N. Filonov, “Absolute continuity of 2D Schrödinger operator with partially periodic coefficients”, Algebra i Analiz, 29:2 (2017),  220–241  mathnet  mathscinet  elib; St. Petersburg Math. J., 29:2 (2018), 383–398  isi  scopus 2
2014
13. A. Prohorov, N. Filonov, “Regularity of electromagnetic fields in convex domains”, Zap. Nauchn. Sem. POMI, 425 (2014),  55–85  mathnet; J. Math. Sci. (N. Y.), 210:6 (2015), 793–813  scopus 5
2013
14. N. Filonov, “Weyl asymptotics for the spectrum of the Maxwell operator in Lipschitz domains of arbitrary dimension”, Algebra i Analiz, 25:1 (2013),  170–215  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 25:1 (2014), 117–149  isi 2
15. N. Filonov, “On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$”, Zap. Nauchn. Sem. POMI, 410 (2013),  168–186  mathnet  mathscinet; J. Math. Sci. (N. Y.), 195:1 (2013), 98–108  scopus 12
2010
16. Yu. G. Safarov, N. D. Filonov, “Asymptotic Estimates of the Difference Between the Dirichlet and Neumann Counting Functions”, Funktsional. Anal. i Prilozhen., 44:4 (2010),  54–64  mathnet  mathscinet  zmath; Funct. Anal. Appl., 44:4 (2010), 286–294  isi  scopus 3
17. I. Kachkovskii, N. Filonov, “Absolute continuity of the spectrum of the periodic Scrödinger operator in a layer and in a smooth cylinder”, Zap. Nauchn. Sem. POMI, 385 (2010),  69–82  mathnet; J. Math. Sci. (N. Y.), 178:3 (2011), 274–281  scopus 6
2009
18. I. Kachkovskii, N. Filonov, “Absolute continuity of the spectrum of a periodic Schrödinger operator in a multidimensional cylinder”, Algebra i Analiz, 21:1 (2009),  133–152  mathnet  mathscinet  zmath; St. Petersburg Math. J., 21:1 (2010), 95–109  isi  scopus 16
19. N. Filonov, T. Shilkin, “On the Stokes problem with nonzero divergence”, Zap. Nauchn. Sem. POMI, 370 (2009),  184–202  mathnet; J. Math. Sci. (N. Y.), 166:1 (2010), 106–117  scopus 5
2006
20. A. B. Alekseev, M. Sh. Birman, N. D. Filonov, “Spectrum asymptotics for one “nonsmooth” variational problem with solvable constraint”, Algebra i Analiz, 18:5 (2006),  1–22  mathnet  mathscinet  zmath; St. Petersburg Math. J., 18:5 (2007), 681–697 3
2004
21. M. Tikhomirov, N. Filonov, “Absolute continuity of an even periodic Schrödinger operator with nonsmooth coefficients”, Algebra i Analiz, 16:3 (2004),  201–210  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:3 (2005), 583–589 16
22. N. Filonov, “An inequality for eigenvalues of the Dirichlet and Neumann problems for the Laplace operator”, Algebra i Analiz, 16:2 (2004),  172–176  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:2 (2005), 413–416 47
23. N. Filonov, A. V. Sobolev, “Absence of the singular continuous component in the spectrum of analytic direct integrals”, Zap. Nauchn. Sem. POMI, 318 (2004),  298–307  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 136:2 (2006), 3826–3831 25
1999
24. N. Filonov, “Spectral analysis of the selfadjoint operator rot in a domain of finite measure”, Algebra i Analiz, 11:6 (1999),  178–190  mathnet  mathscinet  zmath; St. Petersburg Math. J., 11:6 (2000), 1085–1095 5
25. N. D. Filonov, “The operator rot in an arbitrary region of finite measure”, Zap. Nauchn. Sem. POMI, 262 (1999),  227–230  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 110:5 (2002), 3029–3030 1
1997
26. N. Filonov, “Principal singularities of the magnetic field component in resonators with a boundary of a given class of smoothness”, Algebra i Analiz, 9:2 (1997),  241–255  mathnet  mathscinet  zmath; St. Petersburg Math. J., 9:2 (1998), 379–390 8
1996
27. N. Filonov, “Principal singularities of the magnetic component of an electromagnetic field in domains with screens”, Algebra i Analiz, 8:3 (1996),  212–236  mathnet  mathscinet  zmath; St. Petersburg Math. J., 8:3 (1997), 525–542 2

Presentations in Math-Net.Ru
1. On the rate of decay at infinity of solutions to the Schrödinger equation in a cylinder domains
N. Filonov
Friends in Partial Differential Equations
May 25, 2024 10:00   
2. Гипотеза Пойа для задачи Дирихле в многомерном шаре
N. D. Filonov
Traditional session of MIAN-PDMI "Differential Equations and Dynamical Systems"
May 12, 2023 15:30   
3. The Polya conjecture for the Dirichlet problem in a multidimensional ball
N. D. Filonov
V. I. Smirnov Seminar on Mathematical Physics
October 3, 2022 15:00
4. On the rate of decrease at infinity for solutions to the Schrödinger equation in a half-cylinder (on a joint research with S.Krymskii)
N. D. Filonov
V. I. Smirnov Seminar on Mathematical Physics
April 12, 2021 16:30   
5. Неравенства для собственных чисел задач Дирихле и Неймана для оператора Лапласа
N. D. Filonov
Seminar of Chebyshev Laboratory on Spectral Theory
April 27, 2012 15:00

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