Vladimir A. ZOLOTAREV

(Vladimir ZOLOTAREV)

 
 
Mathematical Division
47 Lenin ave.
Kharkiv, 61103,
UKRAINE
 
Tel: +38057-340-0966
 
     
 
 
   
 
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Curriculum Vitae

Date of Birth:

 

October 6, 1951.

  

 
Citizenship:

 

Ukrainian

  

 
Education:

 

M.S.

  

Faculty of Mechanics and Mathematics, Kharkiv National University, June 18, 1973;

Ph.D.

  

Kharkiv National  University, October 6, 1978. Title: "Multidimensional triangular models of systems of linear operators". Supervisor M. S. Livsic

 

D.Sc.

  

Kharkiv National  University, October 31, 1994. Title: "Model representations of Lie algebras of linear non-selfadjoint operators". 
Permanent Positions:

 

02.2010 till now

 

Leading Research Fellow,  Mathematical Division, Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine;

 

 12.1994-02.2010   Full Professor, Dept. of Higher Mathematics and Informatics, Kharkiv National University 

 

 05.1983-12.1994   Assotiate Professor, Dept. of Higher Mathematics and Informatics, Kharkiv National University 
10.1983-12.1994   Senior lecturer, Dept. of General Mathematics, Kharkiv National University 

 

 11.1976-10.1983   Senior lecturer, Dept. of General Mathematics, Kharkiv National University 
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Research interests:

FUNCTIONAL ANALYSIS AND THEORY OF FUNCTIONS:

 

 Models of Representation of Operator Systems,

 

 Scattering Theory,

 

 Riemann Surfaces,

 

 Random Processes.
  Inverse Problems
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List of principal publications

Monograph

  1. Zolotarev, V. A. Analytic Methods of Spectral Representations of Non-Selfadjoint (Non-Unitary) Operators. 2nd Edition. Springer Cham, Series Lecture Notes in Mathematics, volume 2355, 2025, xiv + 537 pp.
  2. Zolotarev, V. A. Analytic Methods of Spectral Representations of Non-Selfadjoint and Non-Unitary Operators. Kyiv: Akademperiodyka, 2020. — 433 pp
  3. Zolotarev V. A., Commutative systems of non-self-adjoint (non-unitary) operators and its model representations, “Serednyak”, Kharkiv National University Publ., 2014, 671 pp.
  4. Zolotarev V. A., Analytical methods of spectral representations of non-selfadjoint and non-unitary operators. Kharkiv National University Publ., 2003, 342 pp.

Papers

  1. Zolotarev, V. A. Inverse scattering problem for third order differential operators with local potential on the whole axis. Journal of Mathematical Analysis and Applications, 2025, 546 (2), 129331.
  2. Zolotarev, V. A. Inverse scattering problem for a third-order operator with local potential. Journal of Differential Equations, 2024, 379, pp. 207 – 257.
  3. Zolotarev, V. A. Inverse spectral problem for a third-order differential operator on a finite interval. Journal of Differential Equations, 2024, 396, pp. 102 – 146.
  4. Zolotarev, V. A. Inverse spectral problem for a third-order differential operator. arXiv 2308.11575 v1[math.CA], Aug 2023, 1 – 53.
  5. Zolotarev, V. A. Inverse scattering problem for a third-order operator with non-local potential. Journal of Differential Equations, 2023, 358, pp. 1–40
  6. Zolotarev, V. A. Characteristic function of pencils. Model representations of a quadratic operator pencil. arXiv: 2204.12236 v.1 (math.FA), 1 – 44 pp., 2022.
  7. V. A. Zolotarev, Direct and inverse problems for a periodic problem with non-local potential J. Differential Equations 270 (2021) 1 – 23 2.
  8. V. A. Zolotarev, Direct and inverse spectral problems for a Dirac operator with non-local potential J. Math. Anal. Appl. 503 (2021) 125075
  9. Zolotarev V. A., Inverse spectral problem for a third-order differential operator with non-local potential, 2012.00450.pdf (arxiv.org), 2020, 26 pp.
  10. Zolotarev V. A., Direct spectral problems for a Dirac operator with non-local potential, 2010.12287.pdf (arxiv.org), 2020, 23 pp.
  11. Zolotarev V. A., Direct and inverse problems for a periodic problem with non-local potential, 2001.05771.pdf (arxiv.org), 2020, 24 pp.
  12. Berezhnoy Yu. A., Zolotarev V. A. de Haas – van Alpen effect and oscillation on the metal magnetization // J. of Low Temperature Physics, 2018, v. 142, No. ½, 1 – 11.
  13. Zolotarev V. A., Inverse spectral problem for the operators with non-local potential // Mathem. Nachrichten, 2019, vol. 292, no. 3, 661 – 681.
  14. Hatamleh R. and Zolotarev, V. A. Jacobi operators and orthonormal matrix-valued polynomials. II. Ukr. Math. J., 2017, Vol. 69, No. 6, 836 – 847.
  15. Hatamleh R. and Zolotarev, V. A. Jacobi operators and orthonormal matrix-valued polynomials. I. Ukr. Math. J., 2017, Vol. 69, No. 3, 228 – 239.
  16. Hatamleh, R. and Zolotarev, V. A. On the abstract inverse scattering problem for trace class perturbations J. of Math. Physics, Analysis and Geometry, 2017, Vol. 13, Issue 1, 3 – 34.
  17. Hatamleh R., Zolotarev V. A. Triangular models of commutative systems of linear operators close to unitary ones // UMJ, 2016, vol. 68, no. 5, 694 – 711.
  18. Hatamleh, R. and Zolotarev, V. A. On model representations of non-selfadjoint operators with infinitely dimensional imaginary component. J. of Math. Physics, Analysis and Geometry, 2015, Vol. 11, No. 2, 174 – 189.
  19. Zolotarev, V. A. Scattering problem for operators with non-local potential. Mat. Sb., 2014, Vol. 205, No. 11, 40 – 74 (in Russian).
  20. Zolotarev, V. A. and Hatamleh, R. On two-dimensional model representations of one class of commuting operators. Ukr. Math. J., 2014, Vol. 66, No. 1, 108 – 127.
  21. Zolotarev, V. A. Direct and inverse problems for an operator with non-local potential. Sbornik: Mathematics, 2012, Vol. 203, No. 12, 1785 – 1807.
  22. Zolotarev, V. A. On a certain class of commuting systems of linear operators. Functional Analysis and Its Applications, 2012, Vol. 46, Issue 4, 308 – 312.
  23. Hatamleh R., Zolotarev V. A., On the universal model of commutative systems of linear operators // J. of Math. Physics, Analysis, Geometry, 2012, vol. 8, no. 3, 248 – 259.
  24. Zolotarev, V. A. Model representations for systems of selfadjoint operators satisfying commutation relations. Sbornik: Mathematics, 2010, Vol. 201, No. 10, 1461 – 1495.
  25. Zolotarev V. A., Properties of characteristic function of commutative system of unbounted nonselfadjoint operators, Journal of Math. Phys., Anal., Geom., 2010, Vol. 6, No. 2, 192-228.
  26. Zolotarev V. A., Hatamleh R., Potapov –Ginsburg transformation and functional models of non-dissipative operators, Serdica Math. J., 2009, Vol. 35, 343-358.
  27. Zolotarev V. A., On commutative systems of nonselfadjoint unbounded linear operators, Journal of Math. Phys., Anal., Geom., 2009, Vol. 5, No. 3, 275-295.
  28. Zolotarev V. A., Functional models for commutative systems of linear operators, Matem. Sb., 2009, Vol. 200, No. 3, 31-48 (in Russian); engl. translation in Sbornik: Mathematics, 2009, Vol. 5, No. 3, 339-356.
  29. Zolotarev V. A., Functional models of commutative operator systems, Journal of Math. Phys., Anal., Geom., 2008, Vol. 4, No. 3, 420-440.
  30. Zolotarev V., Hatamleh R., On connection between characteristic functions and the Caratheodori class functions, Serdica math. j., 2006, Vol. 32, 289-302.
  31. Zolotarev V. A., Scattering scheme with many parameters and translational models of commutative operator systems,Journal of Math. Phys., Anal., Geom., 2007, Vol. 3, No. 4, 424-447.
  32. Zolotarev V. A., Isometric expansions of quantum algebra of linear bounded operatorJournal of Math. Phys., Anal., Geom., 2006, Vol. 2, No. 2, 207-224.
  33. Zolotarev V. A., Rozumenko O. V., Pavlov functional model of bounded non-selfadjoint operator, Visnyk Kharkivs'kogo Natsional'nogo Universytetu, 2006, No. 749, 30-49 (in Russian).
  34. Zolotarev V. A., Isometric dilations of commutative systems of linear operators, Journal of Math. Phys., Anal., Geom., 2006, Vol. 2, No. 2, 192-208.
  35. Zolotarev V. A., Syrovatskiy V. N., De Branges transform relative to circle, Visnyk Kharkivs'kogo Natsional'nogo Universytetu, 2005, No. 701, 80-92 (in Russian).
  36. Zolotarev V. A., On isometric dilations of commutative systems of linear operators , Journal of Math. Phys., Anal., Geom., 2005, Vol. 1, No. 2, 192-208.
  37. Zolotarev V. A., Isometric expansions of commutative operator systems, Matem. Fizika, Analiz, Geometriya, 2004, Vol. 11, No. 3, 282-301 (in Russian)
  38. Zolotarev V. A., L. de Branges spaces and functional models of non-dissipative operators, Matem. Fizika, Analiz, Geometriya., 2002, Vol. 9, No. 4, 622-641 (in Russian).
  39. Zolotarev V. A., Functional model of bounded operator, Matem. Fizika, Analiz, Geometriya., 2001, Vol. 2, No. 2, 158-174 (in Russian).
  40. Zolotarev V. A., Functional models for the Lie algebra SL(2,R) of linear non-selfadjoint operators, D. Alpay and V. Vinnikov (editors), Operator Theory, System Theory and Related Topics (The Moche Livsic Anniversary Volume), Operator Theory: Advance and Applications, 2000, Birkhauser, Basel, 549-578.
  41. Zolotarev V. A., Functional model for Lie algebra ISO(1,1) of linear non-selfadjoint operators, Matem. Sb., 1995, Vol. 186, No. 1, 76-106 (in Russian).
  42. Zolotarev V., Kirchev K., Nonstationary curves in Hilbert spaces and their correlation function, Integr. Equat. Oper. Theory, 1994, Vol. 19, 270-289, 447-457.
  43. Zolotarev V. A., Functional model of a Lie algebra, Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya (Kharkov), 1993, No. 58, 80-86 (in Russian).
  44. Zolotarev V. A., Lax-Fillips scattering scheme on groups and functional models of Lie algebra, Matem. Sb., 1992, Vol. 183, No. 5, 115-144 (in Russian).
  45. Zolotarev V. A., Non-stationary curves in Hilbert spaces and non-linear operator equations, Teoriya Operatorov Subgarmonicheskih Funktsiy (Kyiv), 1991, 54-59 (in Russian).
  46. Zolotarev V. A., Functional models on Riemann surface, Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya (Kharkov), 1991, No.56, 123-128 (in Russian).
  47. Zolotarev V. A., Yantsevich A. A., On one class of nonlinear operator equations with non-selfadjoint second member, Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya (Kharkov), 1991, No. 55, 74-78 (in Russian).
  48. Zolotarev V. A., Time cones and functional model on Riemann surface, Matem. Sb., 1990, Vol. 181, No. 7, 965-994 (in Russian).
  49. Zolotarev V. A., Model representations of commuting systems of linear operators, Funktsionalniy Analiz i Yego Pril., 1988, No. 22, 66-68.
  50. Zolotarev V. A., Universal models of operators with given restrictions on resolvent growth, Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya (Kharkov), 1986, No. 45, 40-45.
  51. Zolotarev V. A., La factorisation des fonctions des operateurs de transmission et la methode de la construction d'operateurs inversible dans L2(0,1), J. Operator Theory., 1984, No. 12, 127-157 (in French).
  52. Zolotarev V. A., La factorisation des fonctions des operateurs de transmission et la methode de la construction d'operateurs inversible dans L2(0,1), Preprint, Lab. d'analyse numerique, Universite, Paris VI, 1983, 46 pp. (in French).
  53. Zolotarev V. A., Le models triangulaires et founctionnels de colligations commutatives unitaires metrique, Preprint, Lab. d'analyse numerique, Universite, Paris VI, 1983, 52 pp. (in French).
  54. Zolotarev V. A., Spectral analysis of non-selfadjoint commutative operator systems and nonlinear differential equations, Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya (Kharkov), 1983, No. 40, 68-71 (in Russian).
  55. Zolotarev V. A., Triangular models of systems of non-commuting operators, Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya (Kharkov), 1979, No. 31, 56-58 (in Russian).
  56. Zolotarev V. A., On triangular models of systems of twice commuting operators, DAN Arm SSR, 1976, Vol. 63, No. 3, 136-140.
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Last modified 02.06.2025