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Lomov, Igor Sergeevich

Statistics Math-Net.Ru
Total publications: 35
Scientific articles: 34

Number of views:
This page:1439
Abstract pages:2393
Full texts:1027
References:82
Professor
Doctor of physico-mathematical sciences (2002)
Birth date: 15.04.1954
E-mail:
Keywords: differential equations, spectrum, eigenvaluie, eigenfunctions, expansions of functions in biorthogonal serieses, small parameter, singular disterbed differential operators.
   
Main publications:
  • Lomov I. S. O lokalnoi skhodimosti biortogonalnykh ryadov, svyazannykh s differentsialnymi operatorami s negladkimi koeffitsientami. 1, 2 // Differentsialnye uravneniya. 2001. T. 37, # 3. S. 328–342; # 5. S. 648–660.
  • Lomov I. S. Usloviya skhodimosti biortogonalnykh funktsii na otrezke // Differentsialnye uravneniya. 2001. T. 37, # 4. S. 562–566.
  • Lomov I. S. Metod spektralnogo razdeleniya peremennykh dlya neregulyarno vyrozhdayuschikhsya ellipticheskikh diffeerntsialnykh operatorov // Doklady RAN. 2001. T. 376, # 5. S. 593–596.

http://www.mathnet.ru/eng/person17511
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/221309

Publications in Math-Net.Ru
2019
1. I. S. Lomov, “The Il'in spectral method for determination of the properties of the basis property and the uniform convergence of biorthogonal expansions on a finite interval”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 19:1 (2019),  34–58  mathnet  elib
2015
2. I. S. Lomov, “Estimates of speed of convergence and equiconvergence of spectral decomposition of ordinary differential operators”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 15:4 (2015),  405–418  mathnet  elib
2005
3. I. S. Lomov, “Convergence of Biorthogonal Expansions of Functions on an Interval for Higher-Order Differential Operators”, Differ. Uravn., 41:5 (2005),  632–646  mathnet  mathscinet; Differ. Equ., 41:5 (2005), 660–676
2003
4. I. S. Lomov, “Integral Representations of a Partial Sum of a Biorthogonal Series for Higher-Order Differential Operators”, Differ. Uravn., 39:5 (2003),  602–611  mathnet  mathscinet; Differ. Equ., 39:5 (2003), 632–643
2002
5. I. S. Lomov, “Uniform Convergence of Biorthogonal Series for the Schrödinger Operator with Multipoint Boundary Conditions”, Differ. Uravn., 38:7 (2002),  890–896  mathnet  mathscinet; Differ. Equ., 38:7 (2002), 941–948
6. I. S. Lomov, “The Method of Spectral Separation of Variables for Degenerating Elliptic Differential Operators”, Differ. Uravn., 38:6 (2002),  795–801  mathnet  mathscinet; Differ. Equ., 38:6 (2002), 839–846
2001
7. I. S. Lomov, “The Local Convergence of Biorthogonal Series Related to Differential Operators with Nonsmooth Coefficients: II”, Differ. Uravn., 37:5 (2001),  648–660  mathnet  mathscinet; Differ. Equ., 37:5 (2001), 680–694
8. I. S. Lomov, “Conditions for Convergence of Biorthogonal Expansions of Functions on a Closed Interval”, Differ. Uravn., 37:4 (2001),  562–565  mathnet  mathscinet; Differ. Equ., 37:4 (2001), 593–597
9. I. S. Lomov, “The Local Convergence of Biorthogonal Series Related to Differential Operators with Nonsmooth Coefficients: I”, Differ. Uravn., 37:3 (2001),  328–342  mathnet  mathscinet; Differ. Equ., 37:3 (2001), 351–366
2000
10. I. S. Lomov, “A Generalized Bessel Inequality for Ordinary Differential Operators with Nonsmooth Coefficients and a Generalization of the Riesz Theorem”, Differ. Uravn., 36:12 (2000),  1621–1630  mathnet  mathscinet; Differ. Equ., 36:12 (2000), 1777–1788
1999
11. I. S. Lomov, “The mean value formula of E. I. Moiseev for even-order differential equations with nonsmooth coefficients”, Differ. Uravn., 35:8 (1999),  1046–1057  mathnet  mathscinet; Differ. Equ., 35:8 (1999), 1054–1066
12. I. S. Lomov, “On estimates for biorthogonal expansions in $\mathcal{L}^p$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, 4,  5–13  mathnet  mathscinet  zmath
1998
13. I. S. Lomov, “On the influence of the degree of summability of coefficients of differential operators on the rate of convergence of spectral expansions. II”, Differ. Uravn., 34:8 (1998),  1066–1077  mathnet  mathscinet; Differ. Equ., 34:8 (1998), 1070–1081
14. I. S. Lomov, “On the influence of the degree of summability of coefficients of differential operators on the rate of equiconvergence of spectral expansions. I”, Differ. Uravn., 34:5 (1998),  619–628  mathnet  mathscinet; Differ. Equ., 34:5 (1998), 621–630
15. I. S. Lomov, “A coefficient condition for the convergence of biorthogonal expansions of functions in $\mathscr L^p(0,1)$”, Differ. Uravn., 34:1 (1998),  31–39  mathnet  mathscinet; Differ. Equ., 34:1 (1998), 29–38
16. I. S. Lomov, “The basis property on compact sets of root functions of second-order differential operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, 4,  40–52  mathnet  mathscinet; Russian Math. (Iz. VUZ), 42:4 (1998), 37–50
1996
17. I. S. Lomov, “On the rate of convergence of biorthogonal expansions of functions”, Differ. Uravn., 32:12 (1996),  1618–1629  mathnet  mathscinet; Differ. Equ., 32:12 (1996), 1611–1622
18. I. S. Lomov, “On the rate of convergence of biorthogonal series connected with second-order differential operators”, Differ. Uravn., 32:1 (1996),  71–82  mathnet  mathscinet; Differ. Equ., 32:1 (1996), 73–84
1995
19. I. S. Lomov, “On the approximation of functions on a segment by spectral expansions of the Schrödinger operator”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, 4,  43–54  mathnet  mathscinet  zmath
1993
20. I. S. Lomov, “Small denominators in the analytic theory of degenerate differential equations”, Differ. Uravn., 29:12 (1993),  2079–2089  mathnet  mathscinet; Differ. Equ., 29:12 (1993), 1811–1820
21. I. S. Lomov, “On the basis property of systems of nonregular root vectors of higher-order differential operators”, Differ. Uravn., 29:1 (1993),  74–86  mathnet  mathscinet; Differ. Equ., 29:1 (1993), 62–72
1991
22. I. S. Lomov, “A theorem on the unconditional basis property of root vectors of second-order weighted differential operators”, Differ. Uravn., 27:9 (1991),  1550–1563  mathnet  mathscinet  zmath; Differ. Equ., 27:9 (1991), 1098–1107
23. I. S. Lomov, “The basis property of root vectors of loaded second-order differential operators on an interval”, Differ. Uravn., 27:1 (1991),  80–93  mathnet  mathscinet; Differ. Equ., 27:1 (1991), 64–75
1990
24. I. S. Lomov, “The basis property of root vectors of discontinuous second-order operators in a space of vector-functions”, Differ. Uravn., 26:1 (1990),  160–163  mathnet  mathscinet  zmath
25. I. S. Lomov, “Properties of root functions of the Sturm–Liouville operator that are discontinuous on an everywhere dense set”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, 8,  35–44  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 34:8 (1990), 39–49
1989
26. I. S. Lomov, “The basis property of root functions of operators with multipoint boundary conditions”, Differ. Uravn., 25:6 (1989),  1053–1056  mathnet  mathscinet  zmath
1988
27. I. S. Lomov, “Construction of exact solutions of some singularly perturbed equations”, Differ. Uravn., 24:6 (1988),  1073–1075  mathnet  mathscinet  zmath
1987
28. I. S. Lomov, “Usual convergence of asymptotic series in the presence of zero points of the spectrum”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, 6,  33–40  mathnet  mathscinet  zmath
1985
29. I. S. Lomov, “Estimates of eigen- and associated functions of ordinary differential operators”, Differ. Uravn., 21:5 (1985),  903–906  mathnet  mathscinet  zmath
1982
30. I. S. Lomov, “Some properties of eigen- and associated functions of the Sturm–Liouville operator”, Differ. Uravn., 18:10 (1982),  1684–1694  mathnet  mathscinet
31. I. S. Lomov, “Rate of equiconvergence of Fourier series in eigenfunctions of Sturm–Liouville operators in an integral metric”, Differ. Uravn., 18:9 (1982),  1480–1493  mathnet  mathscinet  zmath
1979
32. I. S. Lomov, “Estimates for the eigenfunctions and associated functions of an operator of Sturm–Liouville type”, Dokl. Akad. Nauk SSSR, 248:6 (1979),  1303–1306  mathnet  mathscinet  zmath
33. I. S. Lomov, “Certain properties of spectral decompositions connected with Sturm–Liouville operators”, Dokl. Akad. Nauk SSSR, 248:5 (1979),  1063–1065  mathnet  mathscinet  zmath
1976
34. I. S. Lomov, “The unique solvability of the mixed problem for a hyperbolic equation with complex potential”, Differ. Uravn., 12:10 (1976),  1866–1876  mathnet  mathscinet  zmath

2008
35. O. M. Belotserkovskii, I. S. Lomov, E. I. Moiseev, Yu. S. Osipov, V. A. Sadovnichii, I. A. Shishmarev, “Vladimir Aleksandrovich Il'in (on his 80th birthday)”, Uspekhi Mat. Nauk, 63:6(384) (2008),  173–182  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:6 (2008), 1163–1172  isi

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