Skip to main content
SpringerLink
Log in

The Life and Work of Nikolai Vasilevski

  • Chapter
Recent Trends in Toeplitz and Pseudodifferential Operators

Part of the book series: Operator Theory: Advances and Applications ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Principal publications of Nikolai Vasilevski

Book

  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. Articles

    Google Scholar 

  2. 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. 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. 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. 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. 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. 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. 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. 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.

    MathSciNet  Google Scholar 

  10. 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. 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. 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. 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. 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. 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. 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. 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.

    MathSciNet  Google Scholar 

  18. N.L. Vasilevski. Banach algebras generated by some two-dimensional integral operators. I. Math. Nachr., 1980, b. 96, p. 245–255 (Russian).

    Article  Google Scholar 

  19. 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. 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. 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. 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. 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. . 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.

    MathSciNet  Google Scholar 

  35. 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. N.L. Vasilevski. Toeplitz operators associated with the Siegel domains. Matematicki Vesnik, 1988, v. 40, p. 349–354.

    MathSciNet  Google Scholar 

  37. 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. 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. N.L. Vasilevski, M.V. Shapiro. Some questions of hypercomplex analysis “Complex Analysis and Applications’ 87”, Sofia, 1989, p. 523–531.

    Google Scholar 

  40. 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. 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. N.L. Vasilevski. On an algebra generated by abstract singular operators and a shift operator. Math. Nachr., v. 162, 1993, p. 89–108.

    Article  MATH  MathSciNet  Google Scholar 

  43. 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. 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. 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. 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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  48. 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.

    Article  MATH  MathSciNet  Google Scholar 

  49. N.L. Vasilevski. On an algebra generated by two-dimensional singular integral operators in plane domains. Complex Variables, v. 26, 1994, p. 79–91.

    MATH  MathSciNet  Google Scholar 

  50. 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.

    MATH  MathSciNet  Google Scholar 

  51. 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. 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.

    MATH  MathSciNet  Google Scholar 

  53. 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.

    MATH  MathSciNet  Google Scholar 

  54. 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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  56. 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.

    Article  MATH  MathSciNet  Google Scholar 

  57. 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. Doklady

    Google Scholar 

  58. 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. 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. M.V. Shapiro, N.L. Vasilevski. On the Bergman kernel function in hyperholomorphic analysis, Acta Applicandae Mathematicae, v. 46, 1997, p. 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  61. 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. N.L. Vasilevski. C *-algebras generated by orthogonal projections and their applications. Integral Equations and Operator Theory, v. 31, 1998, p. 113–132.

    Article  MATH  MathSciNet  Google Scholar 

  63. 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. N.L. Vasilevski, On the structure of Bergman and poly-Bergman spaces, Integral Equations and Operator Theory, v. 33, 1999, p. 471–488.

    Article  MATH  MathSciNet  Google Scholar 

  65. N.L. Vasilevski, On Bergman-Toeplitz operators with commutative symbol algebras, Integral Equations and Operator Theory, v. 34, no. 1, 1999, p. 107–126.

    Article  MATH  MathSciNet  Google Scholar 

  66. 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. 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. N.L. Vasilevski, On quaternionic Bergman and poly-Bergman spaces, Complex Variables, v. 41, 2000, p. 111–132.

    MATH  MathSciNet  Google Scholar 

  69. 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. N.L. Vasilevski, Poly-Fock Spaces, Operator Theory. Advances and Applications v. 117, 2000, p. 371–386.

    MathSciNet  Google Scholar 

  71. 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.

    MATH  Google Scholar 

  72. 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. 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. S. Grudsky, N. Vasilevski, Bergman-Toeplitz operators: Radial component influence, Integral Equations and Operator Theory, v. 40, no. 1, 2001, p. 16–33.

    Article  MathSciNet  Google Scholar 

  75. 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.

    Article  MATH  MathSciNet  Google Scholar 

  76. N.L. Vasilevski. Toeplitz Operators on the Bergman Spaces: Inside-the-Domain Effects, Contemporary Mathematics, v. 289, 2001, p. 79–146.

    MathSciNet  Google Scholar 

  77. 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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  79. 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. 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.

    MATH  MathSciNet  Google Scholar 

  81. 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.

    MATH  MathSciNet  Google Scholar 

  82. 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.

    Article  Google Scholar 

  83. 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. 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.

    MATH  MathSciNet  Google Scholar 

  85. 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.

    MATH  MathSciNet  Google Scholar 

  86. 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.

    MATH  MathSciNet  Google Scholar 

  87. 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.

    Article  MATH  MathSciNet  Google Scholar 

  88. 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. 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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  91. 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).

    MATH  Google Scholar 

  92. 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.

    Article  MathSciNet  Google Scholar 

  93. N. Vasilevski. Poly-Bergman spaces and two-dimensional singular integral operators, Operator Theory: Advances and Applications, v. 171, 2007, p. 349–359.

    Article  MathSciNet  Google Scholar 

  94. N. Tarkhanov, N. Vasilevski. Microlocal analysis of the Bochner-Martinelli integral, Integral Equations and Operator Theory, v. 57, 2007, p. 583–592.

    Article  MATH  MathSciNet  Google Scholar 

  95. 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.

    Article  MATH  MathSciNet  Google Scholar 

  96. 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.

    Article  MATH  MathSciNet  Google Scholar 

  97. 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.

    Article  MATH  MathSciNet  Google Scholar 

  98. N. Vasilevski. Commutative algebras of Toeplitz operators and Berezin quantization, Contemporary Mathematics, v. 462, 2008, p. 125–143.

    MathSciNet  Google Scholar 

  99. 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.

    Article  MathSciNet  Google Scholar 

Ph. D. dissertations directed by Nikolai Vasilevski

  1. Rafael Trujillo, Fredholm Theory of Tensor Product of Operator Algebras, Odessa State University, 1986.

    Google Scholar 

  2. Zhelko Radulovich, Algebras of Multidimensional Singular Integral Operators with Discontinuous Symbols with Respect to Dual Variable, Odessa State University, 1991.

    Google Scholar 

  3. Vladimir Kisil, Algebras of Pseudodifferential Operators Associated with the Heisenberg Group, Odessa State University, 1992.

    Google Scholar 

  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. 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. 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. Armando Sánchez Nungaray, Super operadores de Toeplitz en la dos-esfera, CINVESTAV del I.P.N., Mexico City, 2008.

    Google Scholar 

  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 

Download references

Authors
  1. Sergei Grudsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuri Latushkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Shapiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematical Physics, Andrea Razmadze Mathematical Institute, M. Alexidze str. 1, Tbilisi, 0193, Georgia

    Roland Duduchava

  2. National Polytechnic Institute, ESIME Zacatenco, Av. IPN, 07738, Mexico, D.F., Mexico

    Israel Gohberg  & Vladimir Rabinovich  & 

  3. Departamento de Matemáticas, CINVESTAV, Av. I.P.N. 2508 Col. San Pedro Zacatenco Apartado Postal14-740, Mexico, D.F., Mexico

    Sergei M. Grudsky

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Basel AG

About this chapter

Cite this chapter

Grudsky, S., Latushkin, Y., Shapiro, M. (2010). The Life and Work of Nikolai Vasilevski. In: Duduchava, R., Gohberg, I., Grudsky, S.M., Rabinovich, V. (eds) Recent Trends in Toeplitz and Pseudodifferential Operators. Operator Theory: Advances and Applications, vol 210. Springer, Basel. https://doi.org/10.1007/978-3-0346-0548-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation