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TO THE MEMORY OF PROFESSOR NIKOLAI KARAPETIANTS: LIFE AND SCIENTIFIC HERITAGE

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This review article is dedicated to Professor Nikolai Karapetiants on the occasion of the 80th anniversary of his birthday. This article contains a biography of Nikolai Karapetiants, as well as a brief overview of his research.

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References

  1. Karapetiants, N. K.: “On the theory of boundary value problems in the space of generalized functions”, Scientific communications for 1964, Ser. of exact and natural sciences, Rostov–on–Don, 1965, pp. 31-33.

  2. Karapetiants, N. K., Samko, S. G.: “Uravneniya s involyutivnymi operatorami i ikh prilozheniya”, [Equations with involutive operators and their applications], Rostov. Gos. Univ., Rostov-on-Don, 1988.

  3. Karapetiants, N., Samko, S.: Equations with Involutive Operators. Birkhauser. Boston. Basel. Berlin, 2001.

  4. Askhabov, S. N., Karapetiants, N. K.: “Discrete equations of convolution type with monotone nonlinearity”, Differential Equations, 25:10 (1989), pp. 1255–1261.

  5. Askhabov, S. N., Karapetiants, N. K., Yakubov, A. Ya.: “Integral equations of convolution type with power nonlinearity and systems of such equations”, Soviet Math. Dokl., 41:2 (1990), pp. 323–327 (1991).

  6. Askhabov, S. N., Karapetiants, N. K.: “Convolution-type discrete equations with monotonous nonlinearity in complex spaces”, J. Integral Equations Math. Phys., 1:1 (1992), pp. 44–66.

  7. Askhabov, S. N., Karapetiants, N. K., Yakubov, A. Ya.: “Discrete equations of convolution type with power nonlinearity”, Soviet Math. Dokl., 36:2 (1988), pp. 273–276.

  8. Avsyankin, O. G., Karapetyants, N. K.: “Multidimensional integral operators with homogeneous kernels of degree − n”, Dokl. Math., 368:6 (1999), pp. 727–729.

  9. Avsyankin, O. G., Karapetiants, N. K.: “Multidimensional integral operators with homogeneous kernels”, J. Nat. Geom., 16:1-2 (1999), pp. 1–18.

  10. Avsyankin, O. G., Karapetiants, N. K.: “On a class of integral operators with homogeneous kernels in the semiball”, J. Nat. Geom., 17:1-2 (2000), pp. 1–10.

  11. Avsyankin, O. G., Karapetyants, N. K.: “On the algebra of multidimensional integral operators with homogeneous kernels with variable coefficients”, Russian Math., 45:1 (2001), pp. 1–8.

  12. Avsyankin, O. G., Karapetyants, N. K.: “On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree − n”, Siberian Math. J., 44:6 (2003), pp. 935–950.

  13. Avsyankin, O. G., Karapetyants, N. K.: “Projection Method in the Theory of Integral Operators with Homogeneous Kernels”, Math. Notes, 75:2 (2004), pp. 149–157.

  14. Dybin, V. B., Karapetyants, N. K.: “Integral equations of the convolution type in a class of generalized functions”, Siberian Math. J., 7:3 (1966), pp. 429–440.

  15. Dybin, V. B., Karapetyants, N. K.: “Application of the normalization method to a class of infinite systems of linear algebraic equations”, Izv. VUZov. Matematika, 65:10 (1967), pp. 39–49.

  16. Gil’, A. V., Karapetiants, N. K.: “An integral operator with a homogeneous kernel in the space of functions with bounded mean oscillation”, Dokl. Akad. Nauk, 397:1 (2004), pp. 12–15.

  17. Gil’, A. V., Karapetiants, N. K.: “An integral operator with a homogeneous kernel in the space BMOk of functions”, Dokl. Akad. Nauk, 400:6 (2005), pp. 727–730.

  18. Karapetiants, N. K.: “The normalization of discrete equations of convolution type”, Izv. VUZov. Matematika, 79:12 (1968), pp. 45–52.

  19. Karapetiants, N. K.: “Discrete convolution type equations in a certain exceptional case”, Siberian Math. J., 11:1 (1970), 0. 66–74.

  20. Karapetiants, N. K.: “A certain class of discrete convolution operators with oscillating coefficients”, Dokl. Akad. Nauk SSSR, 216 (1974), pp. 28–31.

  21. Karapetiants, N. K.: “Factorization with the shift x + α on the real line”, Izv. Severo-Kavkaz. Naučn. Centra Vysš. Školy Ser. Estestv. Nauk, 4 (1975), pp. 98–100.

  22. Karapetiants, N. K.: “A class of shift operators”, Izv. Severo-Kavkaz. Naučn. Centra Vysš. Školy Ser. Estestv. Nauk., 3 (1976), pp. 11–12.

  23. Karapetiants, N. K.: “A class of singular functional operators”, Izv. Akad. Nauk Armjan. SSR Ser. Mat., 12:3 (1977), pp. 165–177.

  24. Karapetiants, N. K.: “The Wiener-Hopf integral equation with a symbol that has a zero of fractional order”, Differencial’nye Uravnenija, 13:8 (1977), pp. 1471–1478.

  25. Karapetiants, N. K.: “On the question of complete continuity of operators of convolution type”, Izv. VUZov. Matematika, 11 (1980), pp. 41–49.

  26. Karapetiants, N. K.: “Necessary conditions for boundedness of an operator with a nonnegative quasihomogeneous kernel”, Mat. Zametki, 30:5 (1981), pp. 787–794.

  27. Karapetiants, N. K.: “Complete continuity of some classes of operators of convolution type with homogeneous kernels”, Izv. VUZov. Matematika, 11 (1981), pp. 71–74.

  28. Karapetiants, N. K.: “Integral operators with coordinate-homogeneous kernels”, Soobshch. Akad. Nauk Gruzin. SSR, 105:3 (1982), pp. 469–472.

  29. Karapetiants, N. K.: “Local properties of the solution of the Wiener-Hopf equation”, Izv. VUZov. Matematika, 4 (1983), pp. 61–67.

  30. Karapetiants, N. K.: “Some classes of completely continuous integral operators with homogeneous kernels”, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk, 2 (1986), pp. 45–51.

  31. Karapetiants, N. K.: “On the connection between the Noethericity and the spectrum of an operator acting in a Banach space and in a subspace”, Soobshch. Akad. Nauk Gruzin. SSR, 124:3 (1986), pp. 477–480.

  32. Karapetiants, N. K.: “On an analogue of a theorem of Hörmander for domains different from \(\mathbb {R}^{n}\)”, Dokl. Akad. Nauk SSSR, 293:6 (1987), pp. 1294–1297.

  33. Karapetiants, N. K.: “Complete continuity of convolution operators and operators with homogeneous kernels in Hölder classes”, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk., 2 (1987), pp. 34–39, 140–141.

  34. Karapetiants, N. K.: “Convolution operators in Lipschitz classes. (Russian. English, Armenian summaries)”, Izv. Akad. Nauk Armyan. SSR Ser. Mat., 24:4 (1989), pp. 364–376, 416; translation in Soviet J. Contemporary Math. Anal., 24:4 (1989), pp. 52–64.

  35. Karapetiants, N. K.: “A scheme for studying semi-Noethericity of a class of operators”, Soviet Math., 34:2 (1990), pp. 72–76.

  36. Karapetiants, N. K.: “Weighted estimates for the Hardy operator”, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk., 1 (1990), pp. 46–52.

  37. Karapetiants, N. K.: “Local estimates for fractional integral operators and potentials”, Operator theory for complex and hypercomplex analysis (Mexico City, 1994), pp. 137–142, Contemp. Math., 212, Amer. Math. Soc., Providence, RI, 1998.

  38. Karapetiants, N. K.: “On behaviour of the norms of fractional integrals of large orders”, Fract. Calc. Appl. Anal., 5:3 (2002), pp. 295–302.

  39. Karapetiants, N. K., Askhabov, S. N., Yakubov, A. Ya.: “A nonlinear equation of convolution type”, Differentsial’ nye Uravneniya, 22:9 (1986), pp. 1606–1609.

  40. Karapetiants, N. K., Gil’, A. V.: “On a certain integral operator with a homogeneous kernel in the space of functions with bounded mean oscillation”, Integral Transforms Spec. Funct., 16:5-6 (2005), pp. 423–435.

  41. Karapetiants, N. K., Ginsburg, A. I.: “Fractional integrals and singular integrals in the Hölder classes of variable order”, Integral Transform. Spec. Funct., 2:2 (1994), pp. 91–106.

  42. Karapetiants, N. K., Ginsburg, A. I.: “Fractional integrals in the limit case”, Russian Acad. Sci. Dokl. Math., 48:3 (1994), pp. 449–451.

  43. Karapetiants, N. K., Ginsburg, A. I.: “Local estimates for Riesz potential on the ball”, Turkish J. Math., 19:1 (1995), pp. 19–29.

  44. Karapetiants, N. K., Ginsburg, A. I.: “Lebesgue points for fractional integral”, Integral Transform. Spec. Funct., 3:3 (1995), pp. 201–210.

  45. Karapetiants, N. K., Ginsburg, A. I.: “Fractional integrodifferentiation in Hölder classes of arbitrary order”, Georgian Math. J., 2:2 (1995), pp. 141–150.

  46. Karapetiants, N. K., Ginzburg, A. I.: “Lebesgue points and fractional integrals”, Dokl. Akad. Nauk, 352:2 (1997), pp. 163–166.

  47. Karapetiants, N. K., Kilbas, A. A., Saigo, M.: “On the solution of nonlinear Volterra convolution equation with power nonlinearity”, J. Integral Equations Appl., 8:4 (1996), pp. 429–445.

  48. Karapetiants, N. K., Murdaev, Kh. M., Yakubov, A. Ya.: “On the isomorphism realized by fractional integrals in generalized Nikol’skiı̆ classes”, Russian Math., 36:9 (1992), pp. 45–54.

  49. Karapetiants, N. K., Mussalaeva, Z. U.: “Weyl fractional integrals in generalized Hölder classes”, Izv. Nats. Akad. Nauk Armenii Mat., 31:6 (1996), pp. 65–86 (1998); translation in J. Contemp. Math. Anal., 31:6 (1996), pp. 58–77 (1997).

  50. Karapetiants, N. K., Mussalaeva, Z. U.: “On the solvability of an integral equation of fractional order in generalized Hölder classes”, Differential Equations, 32:8 (1996), pp. 1107–1114.

  51. Karapetiants, N. K., Ochirova, V. L.: “On a necessary condition for convergence of averages at Lebesgue p-points of a function in Lp”, Russian Math., 40:9 (1996), pp. 24–29 (1997).

  52. Karapetiants, N. K., Ochirova, V. L.: “Necessary conditions for the convergence of averages for large values of the parameter”, Dokl. Akad. Nauk, 357:2 (1997), pp. 165–167.

  53. Karapetiants, N. K., Rubin, B. S.: “Riesz radial potentials on the disc and fractional integration operators”, Dokl. Akad. Nauk SSSR, 263:6 (1982), pp. 1299–1302.

  54. Karapetiants, N. K., Rubin, B. S.: “Operators of fractional integration in spaces with a weight”, Izv. Akad. Nauk Armyan. SSR, Ser. Mat., 19:1 (1984), pp. 31–43.

  55. Karapetiants, N. K., Rubin, B. S.: “Fractional integrals with a limit index”, Soviet Math., 32:3 (1988), pp. 98–10.

  56. Karapetiants, N. K., Saigo, M., Samko, S. G.: “Upper and lower bounds for solutions of nonlinear Volterra convolution integral equations with power nonlinearity”, J. Integral Equations Appl., 12:4 (2000), pp. 421–448.

  57. Karapetiants, N. K., Samko, S. G.: “A certain class of convolution type integral equations, and its application”, Dokl. Akad. Nauk SSSR, 193 (1970), pp. 981–984.

  58. Karapetiants, N. K., Samko, S. G.: “The index of certain classes of integral operators”, Dokl. Akad. Nauk SSSR, 194 (1970), pp. 504–507.

  59. Karapetiants, N. K., Samko, S. G.: “The functional equation ψ(x + α) − b(x)ψ(x) = g(x)”, Izv. Akad. Nauk Armjan. SSR, Ser. Mat. 5 (1970), pp. 441–448.

  60. Karapetiants, N. K., Samko, S. G.: “On a class of integral equations of convolution type and its applications”, Izv. Math., 5:3 (1971), pp. 731–744.

  61. Karapetiants, N. K., Samko, S. G.: “The discrete Wiener-Hopf operators with oscillating coefficients”, Dokl. Akad. Nauk SSSR, 200 (1971), pp. 17–20.

  62. Karapetiants, N. K., Samko, S. G.: “A certain new approach to the investigation of singular integral equations with a shift”, Dokl. Akad. Nauk SSSR, 202 (1972), pp. 273–276.

  63. Karapetiants, N. K., Samko, S. G.: “Singular integral operators on the axis with a fractional linear shift of Carleman type and the Noether property for operators containing an involution”, Izv. Akad. Nauk Armjan. SSR, Ser. Mat. 7:1 (1972), pp. 68–77.

  64. Karapetiants, N. K., Samko, S. G.: “Singular integral operators with shift on an open contour”, Dokl. Akad. Nauk SSSR, 204 (1972), pp. 536–539.

  65. Karapetiants, N. K., Samko, S. G.: “The index of certain classes of integral operators”, Izv. Akad. Nauk Armjan. SSR, Ser. Mat. 8:1 (1973), pp. 26–40.

  66. Karapetiants, N. K., Samko, S. G.: “Singular integral equations with Carleman shift in the case of discontinuous coefficients, and a study of whether a certain class of linear operators with involution is Noetherian”, Dokl. Akad. Nauk SSSR, 211 (1973), pp. 281–284.

  67. Karapetiants, N. K., Samko, S. G.: “Singular convolution operators with discontinuous symbol”, Siberian Math. J., 16 (1975), pp. 44–61.

  68. Karapetiants, N. K., Samko, S. G.: “Singular integral operators with Carleman shift in the case of piecewise continuous coefficients. I”, Russian Math., 19:2 (1975), pp. 34–43.

  69. Karapetiants, N. K., Samko, S. G.: Singular integral operators with Carleman shift in the case of piecewise continuous coefficients. II”, Russian Math., 19:3 (1975), pp. 25–32.

  70. Karapetiants, N. K., Samko, S. G.: “Discrete convolution operators with coefficients that become almost stable”, Mat. Zametki, 22:3 (1977), pp. 339–344.

  71. Karapetiants, N. K., Samko, S. G.: “A study of the Noethericity of operators with an involution of order n, and its application”, Russian Math., 21:11 (1977), pp. 11–20.

  72. Karapetiants, N. K., Samko, S. G.: “On Fredholm properties of a class of Hankel operators”, Math. Nachr., 217 (2000), pp. 75–103.

  73. Karapetiants, N. K., Samko, S. G.: “Multi-dimensional integral operators with homogeneous kernels”, Fract. Calc. Appl. Anal., 2:1 (1999), pp. 1, 67–96.

  74. Karapetiants, N. K., Samko, S. G.: “On a certain approach to the investigation of equations with involutive operators”, Int. J. Math. Stat. Sci., 8:2 (1999), pp. 135–162.

  75. Karapetiants, N. K., Samko, S. G.: “On multi-dimensional integral equations of convolution type with shift”, Integral Equations Operator Theory, 39:3 (2001), pp. 305–328.

  76. Karapetiants, N. K., Samko, N.: “Weighted theorems on fractional integrals in the generalized Hölder spaces via indices mω and Mω”, Fract. Calc. Appl. Anal., 7:4 (2004), pp. 437–458.

  77. Karapetiants, N. K., Shankishvili, L. D. : “Fractional integrals of imaginary order in the Hölder space on a segment”, Dokl. Akad. Nauk, 364:6 (1999), pp. 738–740.

  78. Karapetiants, N. K., Shankishvili, L. D.: “A short proof of Hardy-Littlewood-type theorem for fractional integrals in weighted Hölder spaces”, Fract. Calc. Appl. Anal., 2:2 (1999), pp. 177–192.

  79. Karapetiants, N. K., Shankishvili, L. D.: “Fractional integro-differentiation of the complex order in generalized Holder spaces \(H_{0}^{{\omega }} ([0, 1], {\rho })\)”, Integral Transforms Spec. Funct., 13:2 (2002), pp. 199–209.

  80. Karapetiants, N. K., Shankishvili, L. D.: “Fractional integrals of imaginary order in the space of Hölder functions with a power weight on an interval”, Math. Notes, 74:1-2 (2003), pp. 49–55.

  81. Karapetiants, N. K., Yakubov, A. Ya.: “A convolution equation with a power nonlinearity of negative order”, Soviet Math. Dokl., 44:2 (1992), pp. 517–520.

  82. Vakulov, B. G., Karapetiants, N. K.: “Potential-type operators on a sphere with singularities on the poles”, Dokl. Akad. Nauk, 392:2 (2003), pp. 151–154.

  83. Vakulov, B. G., Karapetiants, N. K., Shankishvili, L. D.: “Spherical hypersingular operators of imaginary order and their multipliers”, Fract. Calc. Appl. Anal., 4:1 (2001), pp. 101–112.

  84. Vakulov, B. G., Karapetiants, N. K., Shankishvili, L. D. : “Spherical potentials of complex order in generalized Hölder spaces”, Izv. Nats. Akad. Nauk Armenii Mat., 36:2 (2001), pp. 54–78 (2002); translation in J. Contemp. Math. Anal., 36:2 (2001), pp. 5–29 (2002).

  85. Vakulov, B. G., Karapetiants, N. K., Shankishvili, L. D.: “Spherical potentials of complex order in generalized weighted Hölder spaces”, Dokl. Akad. Nauk, 382:3 (2002), pp. 301–304.

  86. Vakulov, B. G., Karapetiants, N. K., Shankishvili, L. D.: “Spherical convolution operators with a power-logarithmic kernel in generalized Hölder spaces”, Russian Math., 47:2 (2003), pp. 1–12.

  87. Vinogradova, G. Yu., Karapetiants, N. K.: “Operators of convolution type in Höl classes”, Mathematical analysis and its applications, Rostov. Gos. Univ., Rostov-on-Don, (1983) pp. 310, 116.

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Funding

The research of O. G. Avsyankin was supported by the Regional Mathematical Center of the Southern Federal University with the Agreement No. 075-02-2022-893 of the Ministry of Science and Higher Education of Russia.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics and Computer Sciences, Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Oleg G. Avsyankin

  2. Universidade do Algarve, Faro, Portugal

    Stefan G. Samko

  3. Kh. Ibragimov Complex Institute of Russian Academy of Sciences, Grosny, Russia

    Stefan G. Samko

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Avsyankin, O.G., Samko, S.G. TO THE MEMORY OF PROFESSOR NIKOLAI KARAPETIANTS: LIFE AND SCIENTIFIC HERITAGE. J Math Sci 266, 231–237 (2022). https://doi.org/10.1007/s10958-022-06037-x

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