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The Life and Work of Nikolai Vasilevski

  • Sergei Grudsky
  • Yuri Latushkin
  • Michael Shapiro
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)

Abstract

Nikolai Leonidovich Vasilevski was born on January 21, 1948 in Odessa, Ukraine. His father, Leonid Semenovich Vasilevski, was a lecturer at Odessa Institute of Civil Engineering, his mother, Maria Nikolaevna Krivtsova, was a docent at the Department of Mathematics and Mechanics of Odessa State University.

Keywords

Operator Theory English Translation Toeplitz Operator Bergman Space Bergman Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Principal publications of Nikolai Vasilevski

Book

  1. 1.
    N.L. Vasilevski. Commutative Algebras of Toeplitz Operators on the Bergman Space, Operator Theory: Advances and Applications, Vol. 183, Birkhäuser Verlag, Basel-Boston-Berlin, 2008, XXIX, 417 p. ArticlesGoogle Scholar
  2. 1.
    N.L. Vasilevski. On the Noether conditions and a formula for the index of a class of integral operators. Doklady Akad. Nauk SSSR, 1972, v. 202, No 4, p. 747–750 (Russian). English translation: Soviet Math. Dokl., v. 13, no. 1, 1972, p. 175-179.Google Scholar
  3. 2.
    N.L. Vasilevski. On properties of a class of integral operators in the space Lp. Matemat. Zametki, 1974, v. 16, No 4, p. 529–535 (Russian). English translation: Math. Notes, v. 16, no. 4, 1974, p. 905-909.Google Scholar
  4. 3.
    N.L. Vasilevski. The Noether theory of a class of potential type integral operators. Izvestija VUZov. Matematika, 1974, No 7, p. 12–20 (Russian). English translation: Soviet Math. (Izv. VUZ), v. 18, no. 7, 1974, p. 8-15.Google Scholar
  5. 4.
    N.L. Vasilevski. On the Noetherian theory of integral operators with a polar logarithmic kernel. Doklady Akad. Nauk SSSR, 1974, v. 215, No 3, p. 514–517 (Russian). English translation: Soviet Math. Dokl., v. 15, no. 2, 1974, p. 522-527.Google Scholar
  6. 5.
    N.L. Vasilevski, E.V. Gutnikov. On the symbol of operators forming finitedimensional algebras. Doklady Akad. Nauk SSSR, 1975, v. 221, No 1, p. 18–21 (Russian). English translation: Soviet Math. Dokl., v. 16, no. 2, 1975, p. 271-275.Google Scholar
  7. 6.
    N.L. Vasilevski, G.S. Litvinchuk. Theory of solvability of a class of singular integral equations with involution. Doklady Akad. Nauk SSSR, 1975, v. 221, No 2, p. 269–271 (Russian). English translation: Soviet Math. Dokl., v. 16, no. 2, 1975, p. 318-321.Google Scholar
  8. 7.
    N.L. Vasilevski, M.V. Shapiro. On an algebra generated by singular integral operators with the Carleman shift and in the case of piece-wise continuous coefficients. Ukrainski Matematicheski Zurnal, 1975, v. 27, No 2, p. 216–223 (Russian). English translation: Ukrainian Math. J., v. 27, no. 2, 1975, p. 171-176.Google Scholar
  9. 8.
    N.L. Vasilevski. On a class of singular integral operators with kernels of polarlogarithmic type. Izvestija Akad. Nauk SSSR, ser. matem., 1976, v. 40, No 1, p. 131–151 (Russian). English translation: Math. USSR Izvestija, v. 10, no. 1, 1976, p. 127-143.MathSciNetGoogle Scholar
  10. 9.
    N.L. Vasilevski, E.V. Gutnikov. On the structure of the symbol of operators forming finite-dimensional algebras. Doklady Akad. Nauk SSSR, 1976, v. 230, No 1, p. 11–14 (Russian). English translation: Soviet Math. Dokl., v. 17, no. 5, 1976, p. 1225-1229.Google Scholar
  11. 10.
    N.L. Vasilevski, A.A. Karelin, P.V. Kerekesha, G.S. Litvinchuk. On a class of singular integral equations with shift and its applications in the theory of boundary value problems for partial differential equations. I. Differentsialnye Uravnenija, 1977, v. 13, No 9, p. 1692–1700 (Russian). English translation: Diff. Equations, v. 13, no. 9, 1977, p. 1180-1185.Google Scholar
  12. 11.
    N.L. Vasilevski, A.A. Karelin, P.V. Kerekesha, G.S. Litvinchuk. On a class of singular integral equations with shift and its applications in the theory of boundary value problems for partial differential equations. II. Differentsialnye Uravnenija, 1977, v. 13, No 11, p. 2051–2062 (Russian). English translation: Diff. Equations, v. 13, no. 11, 1977, p. 1430-1438.Google Scholar
  13. 12.
    N.L. Vasilevski. Symbols of operator algebras. Doklady Akad. Nauk SSSR, 1977, v. 235, No 1, p. 15–18 (Russian). English translation: Soviet Math. Dokl., v. 18, no. 4, 1977, p. 872-876.Google Scholar
  14. 13.
    N.L. Vasilevski, A.A. Karelin. An investigation of a boundary value problem for the partial differential equation of the mixed type with the help of reduction to the singular integral equation with Carleman shift. Izvestija VUZov. Matematika, 1978, No 3, p. 15–19, (Russian). English translation: Soviet Math. (Izv. VUZ), v. 22, no. 3, 1978, p. 11-15.Google Scholar
  15. 14.
    N.L. Vasilevski, R. Trujillo. On ϕ R-operators in matrix algebras of operators. Doklady Akad. Nauk SSSR, 1979, v. 245, No 6, p. 1289–1292 (Russian). English translation: Soviet Math. Dokl., v. 20, no. 2, 1979, p. 406-409.Google Scholar
  16. 15.
    N.L. Vasilevski, R. Trujillo. On the theory of ϕ R-operators in matrix algebras of operators. Linejnye Operatory, Kishinev, 1980, p. 3–15 (Russian).Google Scholar
  17. 16.
    N.L. Vasilevski. On an algebra generated by some two-dimensional integral operators with continuous coefficients in a subdomain of the unit disc. Journal of Integral Equations, 1980, v. 2, p. 111–116.MathSciNetGoogle Scholar
  18. 17.
    N.L. Vasilevski. Banach algebras generated by some two-dimensional integral operators. I. Math. Nachr., 1980, b. 96, p. 245–255 (Russian).CrossRefGoogle Scholar
  19. 18.
    N.L. Vasilevski. Banach algebras generated by some two-dimensional integral operators. II. Math. Nachr., 1980, b. 99, p. 136–144 (Russian).Google Scholar
  20. 19.
    N.L. Vasilevski. On the symbol theory for Banach operator algebras which generalizes algebras of singular integral operators. Differentsialnye Uravnennija, 1981, v. 17, No 4, p. 678–688 (Russian). English translation: Diff. Equations, v. 17, no. 4, 1981, p. 462-469.Google Scholar
  21. 20.
    N.L. Vasilevski, I.M. Spitkovsky. On an algebra generated by two projectors. Doklady Akad. Nauk UkSSR, Ser. “A”, 1981, No 8, p. 10–13 (Russian).Google Scholar
  22. 21.
    N.L. Vasilevski. On the algebra generated by two-dimensional integral operators with Bergman kernel and piece-wise continuous coefficients. Doklady Akad. Nauk SSSR, 1983, v.271, No 5, p. 1041–1044 (Russian). English translation: Soviet Math. Dokl., v. 28, no. 1, 1983, p. 191-194.Google Scholar
  23. 22.
    N.L. Vasilevski. On certain algebras generated by a space analog of the singular operator with Cauchy kernel. Doklady Akad. Nauk SSSR, 1983, v. 273, No 3, p. 521–524 (Russian). English translation: Soviet Math. Dokl., v. 28, no. 3, 1983, p. 654-657.Google Scholar
  24. 23.
    . N.L. Vasilevski. On an algebra generated by abstract singular operators and Carleman shift. Soobshchenija Akad. Nauk GSSR, 1984, v. 115, No 3, p. 473–476 (Russian).Google Scholar
  25. 24.
    N.L. Vasilevski. On an algebra generated by multivariable Wiener-Hopf operators. Reports of Enlarged Session of Seminars of the I.N. Vekua Institute of Applied Mathematics. Tbilisi, 1985, v. 1, p. 59–62 (Russian).Google Scholar
  26. 25.
    N.L. Vasilevski, M.V. Shapiro. On an analogy of monogenity in the sense of Moisil-Teodoresko and some applications in the theory of boundary value problems. Reports of Enlarged Sessions of Seminars of the I.N. Vekua Institute of Applied Mathematics. Tbilisi, 1985, v. 1, p. 63–66 (Russian).Google Scholar
  27. 26.
    N.L. Vasilevski. Algebras generated by multivariable Toeplitz operators with piece-wise continuous presymbols. Scientific Proceedings of the Boundary Value Problems Seminar Dedicated to 75th birthday of Academician BSSR Academy of Sciences F.D. Gahov. Minsk, 1985, p. 149–150 (Russian).Google Scholar
  28. 27.
    N.L. Vasilevski. Two-dimensional Mikhlin-Calderon-Zygmund operators and bisingular operators. Sibirski Matematicheski Zurnal, 1986, v. 27, No 2, p. 23–31 (Russian). English translation: Siberian Math. J., v. 27, no. 2, 1986, p. 161-168.Google Scholar
  29. 28.
    N.L. Vasilevski. Banach algebras generated by two-dimensional integral operators with Bergman Kernel and piece-wise continuous coefficients. I. Izvestija VUZov, Matematika, 1986, No 2, p. 12–21 (Russian). English translation: Soviet Math. (Izv. VUZ), v. 30, no. 2, 1986, p. 14-24.Google Scholar
  30. 29.
    N.L. Vasilevski. Banach algebras generated by two-dimensional integral operators with Bergman Kernel and piece-wise continuous coefficients. II. Izvestija VUZov, Matematika, 1986, No 3, p. 33–38 (Russian). English translation: Soviet Math. (Izv. VUZ), v. 30, no. 3, 1986, p. 44-50.Google Scholar
  31. 30.
    N.L. Vasilevski. Algebras generated by multidimensional singular integral operators and by coefficients admitting discontinuities of homogeneous type. Matematicheski Sbornik, 1986, v. 129, No 1, p. 3–19 (Russian). English translation: Math. USSR Sbornik, v. 57, no. 1, 1987, p. 1-19.Google Scholar
  32. 31.
    N.L. Vasilevski. On an algebra generated by Toeplitz operators with zero-order pseudodifferential presymbols. Doklady Akad. Nauk SSSR, 1986, v. 289, No 1, p. 14–18 (Russian). English translation: Soviet Math. Dokl., v. 34, no. 1, 1987, p. 4-7.Google Scholar
  33. 32.
    N.L. Vasilevski, M.V. Shapiro. On quaternion Φ-monogenic function. “Methods of solving of the direct and inverse geoelectrical problems”. 1987, p. 54–65 (Russian).Google Scholar
  34. 33.
    N.L. Vasilevski. On an algebra connected with Toeplitz operators on the tube domains. Izvestija Akad. Nauk SSSR, ser. matem., 1987, v. 51, No 1, p. 79–95 (Russian). English translation: Math. USSR Izvestija, v. 30, no.1, 1988, p. 71-87.MathSciNetGoogle Scholar
  35. 34.
    N.L. Vasilevski, R. Trujillo. On C *-algebra generated by almost-periodic twodimensional singular integral operators with discontinuous presymbols. Funkcionalny Analiz i ego Prilogenija, 1987, v. 21, No 3, p. 75–76 (Russian). English translation: Func. Analysis and its Appl., v. 21, no. 3, 1987, p. 235-236.Google Scholar
  36. 35.
    N.L. Vasilevski. Toeplitz operators associated with the Siegel domains. Matematicki Vesnik, 1988, v. 40, p. 349–354.MathSciNetGoogle Scholar
  37. 36.
    N.L. Vasilevski. Hardy spaces associated with the Siegel domains. Reports of Enlarged Sessions of Seminars of the I.N. Vekua Institute of Applied Mathematics. Tbilisi, 1988, v. 3, No 1, p. 48–51 (Russian).Google Scholar
  38. 37.
    N.L. Vasilevski, M.V. Shapiro. Holomorphy, hyperholomorphy Toeplitz operators. Uspehi Matematicheskih Nauk, 1989, v. 44, No 4 (268), p. 226–227 (Russian). English translation: Russian Math. Surveys, v. 44, no. 4, 1989, p. 196-197.Google Scholar
  39. 38.
    N.L. Vasilevski, M.V. Shapiro. Some questions of hypercomplex analysis “Complex Analysis and Applications’ 87”, Sofia, 1989, p. 523–531.Google Scholar
  40. 39.
    N.L. Vasilevski. Non-classical singular integral operators and algebras generated by them. Integral Equations and Boundary Value Problems. World Scientific. 1991, p. 210–215.Google Scholar
  41. 40.
    M.V. Shapiro, N.L. Vasilevski. Singular integral operator in Clifford analysis, Clifford Algebras and Their Applications in Mathematical Physics, Kluwer Academic Publishers, Netherlands, 1992, p. 271–277.Google Scholar
  42. 41.
    N.L. Vasilevski. On an algebra generated by abstract singular operators and a shift operator. Math. Nachr., v. 162, 1993, p. 89–108.zbMATHCrossRefMathSciNetGoogle Scholar
  43. 42.
    R.M. Porter, M.V. Shapiro, N.L. Vasilevski. On the analogue of the \( \partial - problem \) in quaternionic analysis. Clifford Algebras and Their Applications in Mathematical Physics, F. Brackx et al., eds., Kluwer Academic Publishers, Netherlands, 1993, p. 167–173.Google Scholar
  44. 43.
    E. Ramírez de Arellano, M.V. Shapiro, N.L. Vasilevski. Hurwitz pairs and Clifford algebra representations. Clifford Algebras and Their Applications in Mathematical Physics, F. Brackx et al., eds., Kluwer Academic Publishers, Netherlands, 1993, p. 175–181.Google Scholar
  45. 44.
    M.V. Shapiro, N.L. Vasilevski. On the Bergman kernel function in the Clifford analysis. Clifford Algebras and Their Applications in Mathematical Physics, F. Brackx et al., eds., Kluwer Academic Publishers, Netherlands, 1993, p. 183–192.Google Scholar
  46. 45.
    N.L. Vasilevski. On “discontinuous” boundary value problems for pseudodifferential operators. International Conference on Differential Equations, Vol. 1, 2, (Barcelona, 1991), World Sci. Publishing, River Edge, NJ, 1993, p. 953–958.Google Scholar
  47. 46.
    N.L. Vasilevski, R. Trujillo. Convolution operators on standard CR-manifolds. I. Structural Properties. Integral Equations and Operator Theory, v. 19, no. 1, 1994, p. 65–107.zbMATHCrossRefMathSciNetGoogle Scholar
  48. 47.
    N.L. Vasilevski. Convolution operators on standard CR-manifolds. II. Algebras of convolution operators on the Heisenberg group. Integral Equations and Operator Theory, v. 19, no. 3, 1994, p. 327–348.zbMATHCrossRefMathSciNetGoogle Scholar
  49. 48.
    N.L. Vasilevski. On an algebra generated by two-dimensional singular integral operators in plane domains. Complex Variables, v. 26, 1994, p. 79–91.zbMATHMathSciNetGoogle Scholar
  50. 49.
    R.M. Porter, M. Shapiro, N. Vasilevski. Quaternionic differential and integral operators and the \( \partial - problem \). Journal of Natural Geometry, v. 6, no. 2, 1994, p. 101–124.zbMATHMathSciNetGoogle Scholar
  51. 50.
    E. Ramírez de Arellano, M.V. Shapiro, N.L. Vasilevski. Two types of analysis associated to the notion of Hurwitz pairs. Differential Geometric Methods in Theoretical Physics, Ed. J. Keller, Z. Oziewich, Advances in Applied Clifford Algebras, v. 4 (S1), 1994, p. 413–422.Google Scholar
  52. 51.
    M.V. Shapiro, N.L. Vasilevski. Quaternionic Φ-hyperholomorphic functions, singular integral operators and boundary value problems. I. Φ-hyperholomorphic function theory. Complex Variables, v. 27, 1995, p. 17–46.zbMATHMathSciNetGoogle Scholar
  53. 52.
    M.V. Shapiro, N.L. Vasilevski. Quaternionic Φ-hyperholomorphic functions, singular integral operators and boundary value problems. II. Algebras of singular integral operators and Riemann type boundary value problems. Complex Variables, v. 27, 1995, p. 67–96.zbMATHMathSciNetGoogle Scholar
  54. 53.
    N. Vasilevski, V. Kisil, E. Ramirez de Arellano, R. Trujillo. Toeplitz operators with discontinuous presymbols on the Fock space. Russian Math. Doklady, v. 345, no. 2, 1995, p. 153–155 (Russian). English translation: Russian Math. Doklady.Google Scholar
  55. 54.
    E. Ramírez de Arellano, N.L. Vasilevski. Toeplitz operators on the Fock space with presymbols discontinuous on a thick set, Mathematische Nachrichten, v. 180, 1996, p. 299–315.zbMATHCrossRefMathSciNetGoogle Scholar
  56. 55.
    E. Ramírez de Arellano, N.L. Vasilevski. Algebras of singular integral operators generated by three orthogonal projections, Integral Equations and Operator Theory, v. 25, no. 3, 1996, p. 277–288.zbMATHCrossRefMathSciNetGoogle Scholar
  57. 56.
    N. Vasilevski, E. Ramirez de Arellano, M. Shapiro. Hurwitz classical problem and associated function theory. Russian Math. Doklady, v. 349, no. 5, 1996, p. 588–591 (Russian). English translation: Russian Math. DokladyGoogle Scholar
  58. 57.
    E. Ramírez de Arellano, M.V. Shapiro, N.L. Vasilevski. The hyperholomorphic Bergman projector and its properties. In: Clifford Algebras and Related Topics, J. Ryan, Ed. CRC Press, Chapter 19, 1996, p. 333–344.Google Scholar
  59. 58.
    E. Ramirez de Arellano, M.V. Shapiro, N.L. Vasilevski. Hurwitz analysis: basic concepts and connection with Clifford analysis. In: Generalizations of Complex Analysis and their Applications in Physics, J. Lawrynowicz, Ed. Banach Center Publications, V. 37, Warszawa, 1996, p. 209–221.Google Scholar
  60. 59.
    M.V. Shapiro, N.L. Vasilevski. On the Bergman kernel function in hyperholomorphic analysis, Acta Applicandae Mathematicae, v. 46, 1997, p. 1–27.zbMATHCrossRefMathSciNetGoogle Scholar
  61. 60.
    E. Ramírez de Arellano, N.L. Vasilevski. Bargmann projection, three-valued functions and corresponding Toeplitz operators, Contemporary Mathematics, v. 212, 1998, p. 185–196.Google Scholar
  62. 61.
    N.L. Vasilevski. C *-algebras generated by orthogonal projections and their applications. Integral Equations and Operator Theory, v. 31, 1998, p. 113–132.zbMATHCrossRefMathSciNetGoogle Scholar
  63. 62.
    N.L. Vasilevski, M.V. Shapiro. On the Bergman kern-function on quaternionic analysis. Izvestiia VUZov, Matematika, no. 2, 1998, p. 84–88 (Russian). English translation: Russian Math. (Izvestiia VUZ), v. 42, no. 2, 1998, p. 81-85.Google Scholar
  64. 63.
    N.L. Vasilevski, On the structure of Bergman and poly-Bergman spaces, Integral Equations and Operator Theory, v. 33, 1999, p. 471–488.zbMATHCrossRefMathSciNetGoogle Scholar
  65. 64.
    N.L. Vasilevski, On Bergman-Toeplitz operators with commutative symbol algebras, Integral Equations and Operator Theory, v. 34, no. 1, 1999, p. 107–126.zbMATHCrossRefMathSciNetGoogle Scholar
  66. 65.
    E. Ramírez de Arellano, M.V. Shapiro, N.L. Vasilevski. The hyperholomorphic Bergman projector and its properties. In: Clifford Algebras and Related Topics, J. Ryan, Ed. CRC Press, Chapter 19, 1996, p. 333–344.Google Scholar
  67. 66.
    E. Ramírez de Arellano, M.V. Shapiro, N.L. Vasilevski. Hurwitz analysis: basic concepts and connection with Clifford analysis. In: Generalizations of Complex Analysis and their Applications in Physics, J. Lawrynowicz, Ed. Banach Center Publications, v. 37, Warszawa, 1996, p. 209–221.Google Scholar
  68. 67.
    N.L. Vasilevski, On quaternionic Bergman and poly-Bergman spaces, Complex Variables, v. 41, 2000, p. 111–132.zbMATHMathSciNetGoogle Scholar
  69. 68.
    V.S. Rabinovish, N.L. Vasilevski, Bergman-Toeplitz and pseudodifferential operators, Operator Theory. Advances and Applications v. 114, 2000, p. 207–234.Google Scholar
  70. 69.
    N.L. Vasilevski, Poly-Fock Spaces, Operator Theory. Advances and Applications v. 117, 2000, p. 371–386.MathSciNetGoogle Scholar
  71. 70.
    V.V. Kucherenko, N.L. Vasilevski, A shift operator generated by a trigonometric system, Mat. Zametki, v. 67, no. 4, 2000, p. 539–548 (Russian). English translation: Mat. Notes.zbMATHGoogle Scholar
  72. 71.
    N.L. Vasilevski, The Bergman space in tube domains, and commuting Toeplitz operators, Doklady RAN, v. 372, no. 1, 2000, p. 9–12 (Russian). English translation: Doklady Mathematics, v. 61, no. 3, 2000.Google Scholar
  73. 72.
    N.L. Vasilevski. Bergman space on tube domains and commuting Toeplitz operators. In: Proceedings of the Second ISAAC Congress, Volume 2, H.G.W. Begehr et al. (eds.), Kluwer Academic Publishers, The Netherlands, Chapter 163, 2000, p. 1523–1537.Google Scholar
  74. 73.
    S. Grudsky, N. Vasilevski, Bergman-Toeplitz operators: Radial component influence, Integral Equations and Operator Theory, v. 40, no. 1, 2001, p. 16–33.CrossRefMathSciNetGoogle Scholar
  75. 74.
    A.N. Karapetyants, V.S. Rabinovich, N.L. Vasilevski, On algebras of twodimensional singular integral operators with homogeneous discontinuities in symbols, Integral Equations and Operator Theory, v. 40, no. 3, 2001, p. 278–308.zbMATHCrossRefMathSciNetGoogle Scholar
  76. 75.
    N.L. Vasilevski. Toeplitz Operators on the Bergman Spaces: Inside-the-Domain Effects, Contemporary Mathematics, v. 289, 2001, p. 79–146.MathSciNetGoogle Scholar
  77. 76.
    N.L. Vasilevski. Bergman spaces on the unit disk. In: Clifford Analysis and Its Applications F. Brackx et al. (eds.), Kluwer Academic Publishers, The Netherlands, 2001, p. 399–409.Google Scholar
  78. 77.
    S. Grudsky, N. Vasilevski. Toeplitz operators on the Fock space: Radial component effects, Integral Equations and Operator Theory, v. 44, no. 1, 2002, p. 10–37.zbMATHCrossRefMathSciNetGoogle Scholar
  79. 78.
    N.L. Vasilevski. Commutative algebras of Toeplitz operators and hyperbolic geometry. In: Proceedings of the Ukranian Mathematical Congress — 2001, Functional Analysis, Section 11, Institute of Mathematics of the National Academy of Sciences, Ukraine, 2002, p. 22–35.Google Scholar
  80. 79.
    N.L. Vasilevski. Bergman Space Structure, Commutative Algebras of Toeplitz Operators and Hyperbolic Geometry, Integral Equations and Operator Theory, v. 46, 2003, p. 235–251.zbMATHMathSciNetGoogle Scholar
  81. 80.
    S. Grudsky, A. Karapetyants, N. Vasilevski. Toeplitz Operators on the Unit Ball in Cn with Radial Symbols, J. Operator Theory, v. 49, 2003, p. 325–346.zbMATHMathSciNetGoogle Scholar
  82. 81.
    J. Ramírez Ortega, N. Vasilevski, E. Ramírez de Arellano On the algebra generated by the Bergman projection and a shift operator. I. Integral Equations and Operator Theory, v. 46, no. 4, 2003, p. 455–471.CrossRefGoogle Scholar
  83. 82.
    N.L. Vasilevski. Toeplitz operators on the Bergman space. In: Factorization, Singular Operators and Related Problems, Edited by S. Samko, A. Lebre, A.F. dos Santos, Kluwer Academic Publishers, 2003, p. 315–333.Google Scholar
  84. 83.
    J. Ramírez Ortega, E. Ramírez de Arellano, N. Vasilevski On the algebra generated by the Bergman projection and a shift operator. II. Bol. Soc. Mat. Mexicana (3), v. 10, 2004, p. 105–117.zbMATHMathSciNetGoogle Scholar
  85. 84.
    S. Grudsky, A. Karapetyants, N. Vasilevski. Dynamics of properties of Toeplitz operators on the upper half-plane: Hyperbolic case, Bol. Soc. Mat. Mexicana (3), v. 10, 2004, p. 119–138.zbMATHMathSciNetGoogle Scholar
  86. 85.
    S. Grudsky, A. Karapetyants, N. Vasilevski. Dynamics of properties of Toeplitz operators on the upper half-plane: Parabolic case, J. Operator Theory, v. 52, no. 1, 2004, p. 185–204.zbMATHMathSciNetGoogle Scholar
  87. 86.
    S. Grudsky, A. Karapetyants, N. Vasilevski. Dynamics of properties of Toeplitz operators with radial Symbols, Integral Equations and Operator Theory, v. 50, no. 2, 2004, p. 217–253.zbMATHCrossRefMathSciNetGoogle Scholar
  88. 87.
    N.L. Vasilevski. On a general local principle for C *-algebras, Izv.VUZ North-Caucasian Region, Natural Sciences, Special Issue, “Pseudodifferential operators and some problems of mathematical physics”, 2005, p. 34–42 (Russian).Google Scholar
  89. 88.
    S. Grudsky, N. Vasilevski. Dynamics of Spectra of Toeplitz Operators, Advances in Analysis. Proceedings of the 4th International ISAAC Congress. (York University, Toronto, Canada 11-16 August 2003), World Scientific, New Jersey London Singapore, 2005, p. 495–504.Google Scholar
  90. 89.
    S. Grudsky, R. Quiroga-Barranco, N. Vasilevski. Commutative C *-algebras of Toeplitz operators and quantization on the unit disk, J. Functional Analysis, v. 234, 2006, p. 1–44.zbMATHCrossRefMathSciNetGoogle Scholar
  91. 90.
    N.L. Vasilevski, S.M. Grudsky, A.N. Karapetyants. Dynamics of properties of Toeplitz operators on weighted Bergman spaces, Siberian Electronic Math. Reports, v. 3, 2006, p. 362–383 (Russian).zbMATHGoogle Scholar
  92. 91.
    N. Vasilevski. On the Toeplitz operators with piecewise continuous symbols on the Bergman space, In: “Modern Operator Theory and Applications”, Operator Theory: Advances and Applications, v. 170, 2007, p. 229–248.CrossRefMathSciNetGoogle Scholar
  93. 92.
    N. Vasilevski. Poly-Bergman spaces and two-dimensional singular integral operators, Operator Theory: Advances and Applications, v. 171, 2007, p. 349–359.CrossRefMathSciNetGoogle Scholar
  94. 93.
    N. Tarkhanov, N. Vasilevski. Microlocal analysis of the Bochner-Martinelli integral, Integral Equations and Operator Theory, v. 57, 2007, p. 583–592.zbMATHCrossRefMathSciNetGoogle Scholar
  95. 94.
    R. Quiroga-Barranco, N. Vasilevski. Commutative algebras of Toeplitz operators on the Reinhardt domains, Integral Equations and Operator Theory, v. 59, no. 1, 2007, p. 67–98.zbMATHCrossRefMathSciNetGoogle Scholar
  96. 95.
    R. Quiroga-Barranco, N. Vasilevski. Commutative C *-algebras of Toeplitz operators on the unit ball, I. Bargmann-type transforms and spectral representations of Toeplitz operators, Integral Equations and Operator Theory, v. 59, no. 3, 2007, p. 379–419.zbMATHCrossRefMathSciNetGoogle Scholar
  97. 96.
    R. Quiroga-Barranco, N. Vasilevski. Commutative C *-algebras of Toeplitz operators on the unit ball, II. Geometry of the level sets of symbols, Integral Equations and Operator Theory, v. 60, no. 1, 2008, p. 89–132.zbMATHCrossRefMathSciNetGoogle Scholar
  98. 97.
    N. Vasilevski. Commutative algebras of Toeplitz operators and Berezin quantization, Contemporary Mathematics, v. 462, 2008, p. 125–143.MathSciNetGoogle Scholar
  99. 98.
    S. Grudsky, N. Vasilevski. On the structure of the C *-algebra generated by Toeplitz operators with piece-wise continuous symbols, Complex Analysis and Operator Theory, v. 2, no. 4, 2008, p. 525–548.CrossRefMathSciNetGoogle Scholar

Ph. D. dissertations directed by Nikolai Vasilevski

  1. 1.
    Rafael Trujillo, Fredholm Theory of Tensor Product of Operator Algebras, Odessa State University, 1986.Google Scholar
  2. 2.
    Zhelko Radulovich, Algebras of Multidimensional Singular Integral Operators with Discontinuous Symbols with Respect to Dual Variable, Odessa State University, 1991.Google Scholar
  3. 3.
    Vladimir Kisil, Algebras of Pseudodifferential Operators Associated with the Heisenberg Group, Odessa State University, 1992.Google Scholar
  4. 4.
    Josué Ramírez Ortega, Algebra generada por la proyección de Bergman y un operador de translación, CINVESTAV del I.P.N., Mexico City, 1999.Google Scholar
  5. 5.
    Maribel Loaiza Leyva, Algebra generada por la proyección de Bergman y por los operadores de multiplicación por funciones continuas a trozos, CINVESTAV del I.P.N., Mexico City, 2000.Google Scholar
  6. 6.
    Ernesto Prieto Sanabría, Operadores de Toeplitz en la 2-esfera en los espacios de Bergman con peso, CINVESTAV del I.P.N., Mexico City, 2007.Google Scholar
  7. 7.
    Armando Sánchez Nungaray, Super operadores de Toeplitz en la dos-esfera, CINVESTAV del I.P.N., Mexico City, 2008.Google Scholar
  8. 8.
    Carlos Moreno Munoz, Operadores de Toeplitz en el espacio de Bergman con peso: Caso parabólico, CINVESTAV del I.P.N., Mexico City, 2009.Google Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Sergei Grudsky
  • Yuri Latushkin
  • Michael Shapiro

There are no affiliations available

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