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Lomov Igor Sergeevich

Publications in Math-Net.Ru

  1. Summation method for Fourier series associated with a mixed problem for the inhomogeneous telegraph equation

    Zh. Vychisl. Mat. Mat. Fiz., 65:3 (2025),  294–300
  2. Generalized solution of a mixed problem for the wave equation with a nonsmooth right-hand side

    Dokl. RAN. Math. Inf. Proc. Upr., 516 (2024),  26–30
  3. Asymptotic estimates for the solution of the Cauchy problem for a differential equation with linear degeneration

    Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 207 (2022),  37–47
  4. Generalized d'Alembert formula for the telegraph equation

    Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 199 (2021),  66–79
  5. Investigation of singularly perturbed and irregularly degenerate elliptic problems

    Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 191 (2021),  105–114
  6. 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. Math. Mech. Inform., 19:1 (2019),  34–58
  7. Estimates of speed of convergence and equiconvergence of spectral decomposition of ordinary differential operators

    Izv. Saratov Univ. Math. Mech. Inform., 15:4 (2015),  405–418
  8. Convergence of Biorthogonal Expansions of Functions on an Interval for Higher-Order Differential Operators

    Differ. Uravn., 41:5 (2005),  632–646
  9. Integral Representations of a Partial Sum of a Biorthogonal Series for Higher-Order Differential Operators

    Differ. Uravn., 39:5 (2003),  602–611
  10. Uniform Convergence of Biorthogonal Series for the Schrödinger Operator with Multipoint Boundary Conditions

    Differ. Uravn., 38:7 (2002),  890–896
  11. The Method of Spectral Separation of Variables for Degenerating Elliptic Differential Operators

    Differ. Uravn., 38:6 (2002),  795–801
  12. The Local Convergence of Biorthogonal Series Related to Differential Operators with Nonsmooth Coefficients: II

    Differ. Uravn., 37:5 (2001),  648–660
  13. Conditions for Convergence of Biorthogonal Expansions of Functions on a Closed Interval

    Differ. Uravn., 37:4 (2001),  562–565
  14. The Local Convergence of Biorthogonal Series Related to Differential Operators with Nonsmooth Coefficients: I

    Differ. Uravn., 37:3 (2001),  328–342
  15. 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
  16. The mean value formula of E. I. Moiseev for even-order differential equations with nonsmooth coefficients

    Differ. Uravn., 35:8 (1999),  1046–1057
  17. On estimates for biorthogonal expansions in $\mathcal{L}^p$

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 4,  5–13
  18. 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
  19. 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
  20. A coefficient condition for the convergence of biorthogonal expansions of functions in $\mathscr L^p(0,1)$

    Differ. Uravn., 34:1 (1998),  31–39
  21. The basis property on compact sets of root functions of second-order differential operators

    Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 4,  40–52
  22. On the rate of convergence of biorthogonal expansions of functions

    Differ. Uravn., 32:12 (1996),  1618–1629
  23. On the rate of convergence of biorthogonal series connected with second-order differential operators

    Differ. Uravn., 32:1 (1996),  71–82
  24. Approximation of functions on a segment by the spectral resolution of the Schrödinger operator

    Dokl. Akad. Nauk, 342:6 (1995),  735–738
  25. On the approximation of functions on a segment by spectral expansions of the Schrödinger operator

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 4,  43–54
  26. Small denominators in the analytic theory of degenerate differential equations

    Differ. Uravn., 29:12 (1993),  2079–2089
  27. On the basis property of systems of nonregular root vectors of higher-order differential operators

    Differ. Uravn., 29:1 (1993),  74–86
  28. Bessel inequality, Riesz theorem, and unconditional basis property for root vectors of ordinary differential operators

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1992, no. 5,  33–43
  29. A theorem on the unconditional basis property of root vectors of second-order weighted differential operators

    Differ. Uravn., 27:9 (1991),  1550–1563
  30. The basis property of root vectors of loaded second-order differential operators on an interval

    Differ. Uravn., 27:1 (1991),  80–93
  31. The basis property of root vectors of discontinuous second-order operators in a space of vector-functions

    Differ. Uravn., 26:1 (1990),  160–163
  32. Properties of root functions of the Sturm–Liouville operator that are discontinuous on an everywhere dense set

    Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 8,  35–44
  33. The basis property of root functions of operators with multipoint boundary conditions

    Differ. Uravn., 25:6 (1989),  1053–1056
  34. Estimates of root vectors of multipoint spectral problems

    Dokl. Akad. Nauk SSSR, 303:6 (1988),  1304–1306
  35. Necessary and sufficient conditions for the existence of entire analytic solutions of singularly perturbed equations

    Dokl. Akad. Nauk SSSR, 299:4 (1988),  811–815
  36. Construction of exact solutions of some singularly perturbed equations

    Differ. Uravn., 24:6 (1988),  1073–1075
  37. Usual convergence of asymptotic series in the presence of zero points of the spectrum

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 6,  33–40
  38. Estimates of eigen- and associated functions of ordinary differential operators

    Differ. Uravn., 21:5 (1985),  903–906
  39. Some properties of eigen- and associated functions of the Sturm–Liouville operator

    Differ. Uravn., 18:10 (1982),  1684–1694
  40. Rate of equiconvergence of Fourier series in eigenfunctions of Sturm–Liouville operators in an integral metric

    Differ. Uravn., 18:9 (1982),  1480–1493
  41. Estimates for the eigenfunctions and associated functions of an operator of Sturm–Liouville type

    Dokl. Akad. Nauk SSSR, 248:6 (1979),  1303–1306
  42. Certain properties of spectral decompositions connected with Sturm–Liouville operators

    Dokl. Akad. Nauk SSSR, 248:5 (1979),  1063–1065
  43. The unique solvability of the mixed problem for a hyperbolic equation with complex potential

    Differ. Uravn., 12:10 (1976),  1866–1876

  44. Vladimir Aleksandrovich Il'in (on his 80th birthday)

    Uspekhi Mat. Nauk, 63:6(384) (2008),  173–182
  45. Московский государственный университет им. М.В. Ломоносова

    Kvant, 2007, no. 1,  44–52
  46. Московский государственный университет им. М.В. Ломоносова

    Kvant, 2006, no. 1,  44–52
  47. Московский государственный университет им. М.В. Ломоносова

    Kvant, 2005, no. 1,  40–49

© Steklov Math. Inst. of RAS, 2025