Кафедра вищої математики та інформатики

Сергій Михайлович Загороднюк

Загороднюк Сергій Михайлович

Основні лекційні курси для природничих факультетів:

  1. Вища математика;
  2. Інформатика та системологія;
  3. Основи інформатики;
  4. Теорія ймовірностей;

Наукові інтереси:

  1. Теорія операторів у гільбертовому просторі. Узагальнені резольвенти класів операторів. Комплексні симметричні оператори;
  2. Інтерполяційні задачі аналізу. Проблеми моментів;
  3. Теорія ортогональних поліномів. Обернені спектральні задачі;
  4. Нестаціонарні випадкові послідовності у гільбертовому просторі.

Основні наукові результати опубліковані в роботах:

  1. On generalized Jacobi matrices and orthogonal polynomials.—New York J. Math., 9 (2003), 117-136.
  2. Direct and inverse spectral problems for (2N+1)-diagonal, complex, symmetric, non-Hermitian matrices.— Serdica Math. J., 30, No. 4 (2004), 471-482.
  3. On the basic set of solutions of a high-order linear difference equation.— J. Difference Equ. Appl., 12, No. 2 (2006), 213-228.
  4. The direct and inverse spectral problems for (2N+1)-diagonal complex transposition-antisymmetric matrices.— Methods Funct. Anal. Topology, 14, No. 2 (2008), 124-131.
  5. Orthogonal polynomials on rays: properties of zeros, related moment problems and symmetries.— Journal of Mathematical Physics, Analysis, Geometry, 4,No. 3 (2008), 395-419.
  6. Integral representations for spectral functions of some nonself-adjoint Jacobi matrices. — Methods Funct. Anal. Topology, 15, No.1 (2009), 91-100.
  7. Density of polynomials in the $L^2$ space on the real and the imaginary axes and in a Sobolev space. — Serdica Math. J., 35 (2009), 147-168, (соавт. L. Klotz).
  8. On a $J$-polar decomposition of a bounded operator and matrices of $J$-symmetric and $J$-skew-symmetric operators. — Banach J. Math. Anal., 4, No. 2 (2010), 11-36.
  9. Positive definite kernels satisfying difference equations. —Methods Funct. Anal. Topology, 16, No. 1 (2010), 83-100.
  10. A description of all solutions of the matrix Hamburger moment problem in a general case.— Methods Funct. Anal. Topology, 16, No.3 (2010), 271-288.
  11. On the two-dimensional moment problem.— Ann. Funct. Anal., 1, no. 1 (2010), 80-104.
  12. On the complex symmetric and skew-symmetric operators with a simple spectrum.— SIGMA, 7, 016 (2011), 9 pages.
  13. Density of polynomials in some L 2 spaces on radial rays in the complex plane. —Linear Algebra and its Applications, 435 (2011), 128-146, (соавт. F. Marcellan).
  14. Orthogonal polynomials on rays: Christoffel's formula. — Bol. Soc. Mat. Mexicana, 15 (3) (2009), 149-164, (соавт. A.E. Choque Rivero).
  15. The direct and inverse spectral problems for some banded matrices. —Serdica Math. J., 37 (2011), 9-24.
  16. On commuting symmetric operators. —Methods Funct. Anal. Topology, 18, No. 2 (2012), 198-200.
  17. The matrix Stieltjes moment problem: a description of all solutions. — New York J. Math., 18 (2012), 479-497.
  18. The truncated matrix Hausdorff moment problem. —Methods and Applications of Analysis, 19, No. 1 (2012), 21-42.
  19. Devinatz’s moment problem: a description of all solutions. — J. Operator Theory, 68:2 (2012), 515-541.
  20. Generalized resolvents of symmetric and isometric operators: the Shtraus approach. — Annals of Functional Analysis, 4, No. 1 (2013), 175-285.
  21. The Nevanlinna-type formula for the matrix Hamburger moment problem. — Methods Funct. Anal. Topology, 18, no. 4 (2012), 387-400.
  22. The strong matrix Stieltjes moment problem. — Bol. Soc. Mat. Mexicana, 18 3 (2012), 151-169, (соавт. A.E. Choque Rivero).
  23. The two-dimensional moment problem in a strip. — Methods Funct. Anal. Topology, 19, no. 1 (2013), 40-54.
  24. On the density of polynomials in some spaces L2(M). —Mathematical Notes, 95, No. 1 (2014), 53–66.
  25. An algorithm for the truncated matrix Hausdorff moment problem. — Communications in Mathematical Analysis, 17, n. 2 (2014), 108-130, (соавт. A.E. Choque Rivero).
  26. The truncated matrix trigonometric moment problem with an open gap. — Concr. Oper., 2 (2014), 17-26.
  27. Invertible extensions of symmetric operators and the corresponding generalized resolvents. — International Journal of Mathematical Analysis 8, no. 53 (2014), 2639-2649.
  28. Truncated moment problems for J-self-adjoint, J-skew-self-adjoint and J-unitary operators. — Annals of Functional Analysis 6, no. 2 (2015), 91-103.
  29. On the truncated matrix power moment problem with a gap. — Serdica Math. J., 41 Number 2-3 (2015), 199-228.
  30. A refined polar decomposition for $J$-unitary operators. — Sarajevo J. Math., 11(23) no.1 (2015), 65 - 72.
  31. On the truncated operator trigonometric moment problem. — Concr. Oper., 2 (2015), 37 - 46.
  32. On extensions of J-skew-symmetric and J-isometric operators. — Operators and Matrices, 9 n.4 (2015), 847-851.
  33. Unitary extensions of pairs of commuting isometric operators and their generalized resolvents.— New York J. Math., 23 (2017), 555-582.
  34. The Nevanlinna-type parametrization for the operator Hamburger moment problem.— J. Adv. Math. Stud., 10, No. 2 (2017), 183-199.
  35. The inverse spectral problem for Jacobi-type pencils.— SIGMA Symmetry Integrability Geom. Methods Appl., 13, Paper No. 085 (2017), 16 pp.
  36. On the truncated two-dimensional moment problem.— Adv. Oper. Theory, 3, no. 2 (2018), 63-74.
  37. Difference equations related to Jacobi-type pencils.— J. Difference Equ. Appl., 24, no. 10 (2018), 1664-1684.
  38. The operator approach to the truncated multidimensional moment problem.— Concr. Oper., 6 (2019), no. 1, 1-19.
  39. On some classical type Sobolev orthogonal polynomials.— J. Approx. Theory, 250 (2020), 105337.
  40. On a family of hypergeometric Sobolev orthogonal polynomials on the unit circle.— Constructive Mathematical Analysis, 3(2) (2020), 84-75.

Вгору

Основні науково-методичні роботи:

  1. Операторний підхід до матричних проблем моментів (рос. мовою). Методичні вказівки до лекцій та практичних занять студентів 4 курсу механіко-математичного факультету. Х. : ХНУ імені В.Н. Каразіна, 2014.
  2. Ортогональні многочлени на радіальних променях у комплексній площині (рос. мовою). Методичні вказівки до практичних занять та самостійної роботи студентів 4 курсу механіко-математичного факультету. Х. : ХНУ імені В.Н. Каразіна, 2014.

Конференції:

  1. On generalized Jacobi matrices and orthogonal polynomials. Abstracts for the International Conference "Inverse problems and nonlinear equations", Kharkiv, August 12-16, 2002, 93-94.
  2. On a moments problem on rays in the complex plane. Abstracts for the Second International Conference "Mathematical analysis and economics", Sumy, April 1-4, 2003, 58-59.
  3. On the complex moments problem on radial rays. Abstracts for the First Karazin scientific readings, Kharkiv, June 14-16, 2004, 14.
  4. Operators associated with complex symmetric (with respect to the transposition) matrices. Abstracts for the International Conference "Analysis and Topology", Lviv, May 26 - June 7, 2008, 56-57.
  5. Nonself-adjoint Jacobi matrices: the direct and inverse spectral problems, analytic representations of the spectral functions. Abstracts for the International Conference "Analytic Methods of Mechanics and Complex Analysis", Kiev, 29 June - 5 July, 2009, 61-62.
  6. Orthogonal polynomials on radial rays in the complex plane: properties of zeros, Christoffel's formula, related moment problems and symmetries. Ukrainian Mathematical Congress, Kiev, 27 August - 29 August, 2009, electronic.
  7. Density of polynomials in some L 2 spaces on radial rays in the complex plane. Abstracts for the International Conference on Complex Analysis in Memory of A. A. Gol’dberg (1930-2008), Lviv, May 31 — June 5, 2010, 69.
  8. On some matrix moment problems. Abstracts for the International Conference in Modern Analysis, Donetsk, June 20-23, 2011, 52.
  9. Density of polynomials in some L 2 spaces, Abstracts for the International Conference "Complex analysis and its applications" dedicated to the 70th anniversary of A.F. Grishin, Kharkiv, August 15-18, 2011, 43.
  10. On the two-dimensional moment problem, Abstracts for the International Conference "Theory of approximation of functions and its applications" dedicated to the 70th anniversary of Corresponding member of NAS of Ukraine, Profesor A.I. Stepanets, Kamianets-Podilsky, May 28 – June 3, 2012, 140.
  11. The direct and inverse spectral problems for some banded matrices, Abstracts for the International conference "Spectral Theory and Differential Equations (STDE-2012)" in honor of Vladimir A. Marchenko's 90th birthday, Kharkiv, August 20-24, 2012, 117-118.
  12. Koranyi's class of analytic functions and generalized resolvents.Abstracts for the International Conference ``Complex Analysis and Related Topics'', Lviv, May 30 - June 4, 2016, 98-99.
  13. On the truncated two-dimensional moment problem. Abstracts for the International Conference ``Geometry, Differential Equations and Analysis'' in memory of A.V. Pogorelov, Kharkiv, June 17 - June 21, 2019, p. 59.

Вгору