Konstantin A. Makarov

Department of Mathematics, University of Missouri, Columbia, MO 65211


Ph.D. Students

• Vita Borovyk (graduated 2008)

Box approximation and related techniques in spectral theory 

•Anna Skripka (graduated 2007)

Trace formulae in finite von Neumann algebras

• Vladislav V. Melezhik (graduated 1995) 

The quantum few-body scattering problem on singular potentials

• Vasilii A. Buslov (graduated 1992) 

The hierarchy of time scales in the discrete orientation model


Master Students

• Billy Horwitz (graduated 2017)

Rise of Entrophy

• Bryan Novak (graduated 2017)

Inducing stability or instability in the special cases of the swing and pendulum

• Amanda Bright (graduated 2016)

Applications of Brouwer's Fixed Point Theorem

• Aaron Yeager (graduated 2013)

From the Law of Large Numbers to the Quantum Zeno Effect 

•Alexei Kryuchkov (graduated 2004) 

The Extended Matrix-Tree Theorem, Characteristic Polynomials, and Applications



Konstantin A. Makarov, Eduard Tsekanovskii

Dissipative and Non-Unitary Representations and Quantum Measurements

World Scientific, 300 pages, 2022.

Publications and Preprints

89. The Livsic function of a homogeneous  symmetric  operator (with E. Tsekanovskii) (to appear). Oper. Pure and Applied Functional Analysis (2023). 

88. On the invariance principle for a  characteristic function (with E. Tsekanovskii) (to appear). Oper. Theory Adv. Appl. (2022). 

87. On the c-entropy of L-systems with Schrödinger  operator (with S. Belyi, E. Tsekanovskii) 

Complex Anal. Oper. Theory 16 (2022), no. 8, Paper No. 107, 59 pp.

86. Representations of commutation relations in Dissipative Quantum Mechanics, (with E. Tsekanovskii) (preprint), 168 pages (2020). PDF

85. Diagonalization of indefinite saddle point forms, (with L. Grubišic, V. Kostrykin, S. Schmitz, K. Veselic)  Oper. Theory Adv. Appl. Analysis as a Tool in Mathematical Physics 276, 373-400 (2020). 

84. The Tan 2Θ-theorem in fluid dynamics, (with L. Grubišic, V. Kostrykin, S. Schmitz, K. Veselic) J. Spectral Theory 9, 1431-1457 (2019). 

83. On unimodular transformations of conservative L-systems, (with S. Belyi, E. Tsekanovskii), Oper. Theory Adv. Appl. 263, 191-215 (2018). 

82. A system coupling and Donoghue classes of Herglotz-Nevanlinna functions, (with S. Belyi, E. Tsekanovskii), Compl. Anal. Oper. Theory 10(4), 835-880 (2016). 

81. On invariant graph subspaces, (with S. Schmitz, A. Seelmann) Integr. Equ. Oper. Theory 85, 399-425 (2016). 

80. On dissipative and non-unitary solutions to operator commutation relations, (with E. Tsekanovskii) Teoret. Mat. Fiz. 186, 51-75 (2016) translation in Theoret. and Math. Phys. 186, 43-62 (2016). 

79. Convolutions with probability distributions, zeros of L-functions, and the least quadratic nonresidue, (with W. Banks), Functiones et Approximatio 55.2, 243-280 (2016). 

78. Conservative L-systems and the Livsic function(with S. Belyi, E. Tsekanovskii)  Methods Funct. Anal. Topology 21, 104-133 (2015). 

77. On perturbation determinant for antidissipative operators, (with A. Skripka, M. Zinchenko) Integr. Equ. Oper. Theory 81, 301-317 (2015). 

76. On Addition and Multiplication Theorems, (with E. Tsekanovskii) Recent advances in inverse scattering. Shur analysis and stochastic processes, 315-339, Oper. Theory Adv. Appl. 244, Birkhäuser/Springer, Cham, 2015. 

75. Reducing graph subspaces and strong solutions to operator Riccati equations,(with S. Schmitz, A. Seelmann) (preprint).

74. On the Weyl-Titchmarsh and Livsic functions, (with E. Tsekanovskii)  Proceedings of Symposia in Pure Mathematics 87, 291-314 (2013). 

73. The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem, (with A. Seelmann)

J. Reine Angew. Math. 708, 1-15 (2015). 

72. The Tan 2Θ Theorem for indefinite quadratic forms, (with L. Grubišic, V. Kostrykin, K. Veselic) J. Spectr. Theory 3, 83-100 (2013). PDF

71. Representation theorems for indefinite quadratic forms revisited, (with L. Grubišic, V. Kostrykin, K. Veselic) Mathematika 59, 169-189 (2013). 

70. Exponential decay in quantum mechanics, (with V. Kruglov, B. Pavlov,  A. Yafyasov) Computation, physics and beyond, 268-288, Lecture Notes in Comput. Sci., 7160, Springer, Heidelberg, 2012. 

69. On the weak and ergodic limit of the spectral shift function, (with V. Borovyk) Lett. Math. Phys. 100, 1-15 (2012). 

68. The index formula and the spectral shift function for relatively trace class perturbations, Adv. Math. 227, 319-420 (2011). PDF

67. Spectral estimation and inverse initial boundary value problems, Inverse problems and Imaging 4, 1-9 (2010). PDF

66. Some applications of the perturbation determinant in finite von Neumann algebras, Canad. J. Math. 62, 133-156 (2010). PDF

65. Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrodinger operators revisited, Acta. Appl. Math. 103, 315-339 (2008). PDF

64. On Krein's example, (with V. Kostrykin) Proc. Amer. Math. Soc. 136, 2067-2071 (2008). 

63. Evans Functions, Jost Functions, and Fredholm Determinants,(with F. Gesztesy, Yu. Latushkin) Arch. Ration. Mach. Anal. 186, 361-421 (2007). 

62. On μ-scale invariant operators,   (with E. Tsekanovskii) Methods Funct. Anal. Topology 13, 181-186 (2007). PDF

61. The Birman-Schwinger principle in von Neumann algebras of finite type, J. Funct. Anal. 247, 492-508 (2007). PDF

60. Perturbation of spectra and spectral subspaces,  (with V. Kostrykin, A.K. Motovilov) Trans. Amer. Math. Soc. 359, 77-89 (2007). PDF

59. Evans Functions and Modified Fredholm Determinants

58. The adiabatic theorem of Quantum Mechanics and the Riccati equation. PDF

57. The threshold effects for the two-particle Hamiltonians on lattice, Comm. Math. Phys. 262, 91-115 (2006). PDF

56. The singularly continuous spectrum and non-closed invariant subspaces, Oper. Theory Adv. Appl. 160, 299-309 (2005). PDF

55. On the existence of solutions to the operator Riccati equation and the tan Θ theorem, Integr. Equ. Oper. Theory 51, 121-140 (2005). PDF

54. A generalization of the tan 2Θ theorem, Oper. Theory Adv. Appl. 149, 34-372 (2004). PDF

53. (Modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels revisited, Integr. Equ. Oper. Theory 47, 457-497 (2003). PDF

52. Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach, 

 (with V. Kostrykin, A.K. Motovilov)  Contemporary Mathematics 327, Amer. Math. Soc., 181-198 (2003). PDF

51. On a subspace perturbation problem,  (with V. Kostrykin, A.K. Motovilov)  Proc. Amer. Math. 131, Soc. 3469-3476 (2003). 

50. Graph Subspaces and The Spectral Shift Function,  (with S. Albeverio, A.K. Motovilov) Canad. J. Math. 55, 449-503 (2003). PDF

49. SL 2(R), exponential representation of Herglotz functions, and spectral averaging, Algebra i Analiz 15, 104-144 (2003) russPDF; translation in St. Petersburg Math. J, 15, 393-418 (2004). PDF

48. Matrix-valued generalizations of the theorems of Borg and Hochstad, Evolution equations 1-34. Lecture Notes in Pure and Appl. Math.234. Dekker, New York, 2003. PDF

47. Uniqueness results for matrix-valued Schrödinger, Jacobi, and Dirac-type operators, Math. Nachr. 239/240, 103-145 (2002). PDF

46. Some applications of operator-valued Herglotz functions, Oper Theory Adv. Appl.,123, 271-321, (2001). PDF

45. Ahiezer-Kac type Fredholm determinant asymptotics for convolution operators with rational symbols, Trans. Amer. Math. Soc. 353, 1985-1993 (2001). PDF

44. Extension of the Ahiezer-Kac determinant formula to the case of real-valued symbols with two real-valued zeros, Acta Appl. Math. 62, 155-186 (2000). PDF

43. Monotonicity and concavity properties of the spectral shift function, CMS Conf. Proc. 29, 207-222 (2000). PDF

42. Some applications of the spectral shift operator, Operator theory and its applications (Winnipeg, MB, 1998), 267-292, Fields Inst. Commun., 25, Amer. Math. Soc., Providence, RI, 2000. PDF

41. The Ξ operator and its relation to the Krein's spectral shift function, J. Anal. Math. 81, 139-183 (2000). PDF

40. Generalized eigenfunctions under singular perturbations, Methods Funct. Anal. Topology 5, 13-28 (1999).

39. The spectral shift operator, Oper. Theory Adv. Appl. 108, 59-90 (1999). PDF

38. An addendum to Krein's formula, J. Math. Anal. Appl. 222, 594-60 (1998). PDF

37. The Efimov effect and an extended Szeg\"o-Kac limit theorem, Lett. Math. Phys. 43, 73-85 (1998). 

36. Limit behavior in a singular perturbation problem, regularized convolution operators and the three-body quantum problem. Differential and integral operators (Regensburg, 1995), 1-10, Oper. Theory Adv. Appl., 102, Birkhäuser, Basel, 1998. 

35. Nontrivial attractors in a model related to the three-body quantum problem, (with S Albeverio) Acta. Appl. Math. 48, 113-184 (1997).

34. Two sides of a coin: the Efimov Effect and collapse in a three-body system with point interactions. I., Teoret. Mat. Fiz. 107, 415-432 (1996) russPDF; translation in Theoret. and Math. Phys. 107, 755-769 (1997). PDF

33. Attractors in a model related to the three-body quantum problem, C. R. Acad. Sci. Paris. Ser. I Math. 323, 693-698 (1996).

32. Asymptotic spectral analysis of a small diffusion operator and the life times of the corresponding diffusion process, Russian. J. Math. Phys. 4, 341-360 (1996).

31. Point interactions in the problem of three quantum particles with internal structure, Teoret. Mat. Fiz.102, 255-282 (1995) russPDF; translation in Theoret. and Math. Phys. 102, 188-207 (1995). PDF

30. Asymptotic expansions for Fourier transform of singular self-affine measure, J. Math. Anal. Appl. 18, 259-286 (1994). PDF

29. Quantum scattering on a Cantor Bar, J. Math Phys. 35, 1522-1531 (1994). PDF

28. Asymptotics of the Fourier transform of self-affine measures

27. Semiboundedness of the energy operator of a system of three particles with paired interactions of δ -function type, Algebra i Analiz 4, 155-171 (1992) russPD; translation in St. Petersburg Math. J, 4, 967-980 (1993).

26. Life times and lower eigenvalues of an operator of small diffusion, Mat. Zametki 51, 20-31 (1992) russPDF; translation in Math. Notes 51, 14-21 (1992).

25. Point interactions with an internal structure as a limit of separable potentials

24. Point interactions with an internal structure as limits of nonlocal separable potentials

23. Extended Hilbert space approach to few-body problems, J. Math. Phys. 31, 1681–1690 (1990). PDF

22. An extensions theory setting for scattering by breathing bag, J. Math. Phys. 31, 199-201 (1990). PDF

21. The Faddeev method for three-body systems with additional degrees of freedom

20. A resonanting group model with extended channel space

19. Energy-dependent interactions and the extensions theory

18. The operator method for excluding forbidden states

17. Adiabatic representation for Faddeev equations

16. A time-scale hierarchy with small diffusion, Teoret. Mat. Fiz. 76, 219-230 (1988) russPDF; translation in Theoret. and Math. Phys. 76, 818-826 (1989). PDF

15. Algebraic theory of extensions for particles with internal structure

14. The quantum problem of several particles with internal structure. II. The three-body problem, Teoret. Mat. Fiz. 76, 242-260 (1988) russPDF; translation in Theoret. and Math. Phys. 76, 834-847 (1989). PDF

13. The quantum problem of several particles with internal structure. I. The two-body problem, Teoret. Mat. Fiz.75, 431-444 (1996) russPDF; translation in Theoret. and Math. Phys. 75, 630-639 (1988). PDF

12. Scattering on a dynamical quark bag

11. Appendix to the Russian translation of "Solvabale Models in Quantum Mechanics" by S. Albeverio, F. Gesztesy, R. Hoegh Krohn and H. Holden, Moscow, Mir 1991.russPDF

10. Internal degrees of freedom in the Coulomb two-body problem, Teoret. Mat. Fiz. 74, 103-111 (1988) russPDF; translation in Theoret. and Math. Phys. 74, 73-79 (1988). PDF

9. Faddeev equations with additional channels

8. Boundary layer of eigenfunctions of a diffusion operator, Probl. Math. Phys. Wave propagation. Scattering theory. (Ed. by M. Sh. Birman) 12, 41-54 (1987); translation in Amer. Math. Soc. Transl. Ser 2,157, 37-49 (1993). PDF

7. Quantum scattering theory on energy-dependent potentials

6. Model of resonance scattering of compound particles, Teoret. Mat. Fiz. 69, 100-114 (1986). PDF translation in Theoret. and Math. Phys. PDF

5. Discrete orientation model for superparamagnetic particles with cubic symmetry (K > 0), (with G. N. Belozerskii, B.S. Palov, S. G. Simonyan) Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 4, 84-87 (1986). 

4. One-dimensional model of three-particle resonances, Teoret. Mat. Fiz. 63, 78-87 (1985). russPDF translation in Theoret. and Math. Phys. 63, 376-382 (1985). PDF

3. Eigenfunctions of the "small diffusion" operator in the boundary layer approximation, Dokl. Akad. Nauk SSSR 280, 337-342 (1985); Sov. Phys. Dokl. 30, 31-34 (1985). PDF

2. Separation of the spectrum of elliptic operators connected with "small diffusion", Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1, 20-27 (1985). russPDF

1. The discrete orientation model in the theory of superparamagnetism, (with G. N. Belozerskii, B.S. Palov) Vestnik Leningrad. Univ. Fiz. Khim, 4, 12-18 (1982).