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Asymptotic approximation of a logarithmic potential

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Literature Cited

  1. R. Sigurdsson, “Growth properties of analytic and plurisubharmonic functions of finite order,” Math. Scand.,59, No. 2, 235–305 (1986).

    Google Scholar 

  2. R. S. Yulmukhametov, “Asymptotics of plurisubharmonic functions,” Preprint, Akad. Nauk SSSR, Bashkir Branch, Ufa (1986).

    Google Scholar 

  3. V. V. Napalkov and A. B. Sekerin, “Weakly sufficient sets and the representation of analytic functions of several complex variables by Dirichlet series,” Dokl. Akad. Nauk SSSR,260, No. 3, 535–539 (1981).

    Google Scholar 

  4. V. S. Azarin, “On the rays of completely regular growth of an entire function,” Mat. Sb.,79, No. 4, 463–476 (1969).

    Google Scholar 

  5. R. S. Yulmukhametov, “Approximation of subharmonic functions,” [in Russian], Anal. Math. (Budapest),11, No. 3, 257–282 (1985).

    Google Scholar 

  6. A. B. Sekerin, “On integral representation of subharmonic functions,” Mat. Zametki,36, No. 6, 865–871 (1984).

    Google Scholar 

  7. A. B. Sekerin, “Representation of an infinitely differentiable function by a difference of plurisubharmonic functions,” Mat. Zametki,40, No. 5, 598–607 (1986).

    Google Scholar 

  8. A. B. Sekerin, “On integral representation of plurisubharmonic functions,” in: Studies in Approximation Theory [in Russian], Department of Physics and Mathematics, Bashkir Branch, Akad. Nauk SSSR, Ufa (1986), pp. 97–107.

    Google Scholar 

  9. L. Baumgartner, “Beitrage zur Theorie der ganzen Funktionen von zwei complexen Veranderlichen,” Monatsch. Math.,25, No. 1, 18–39 (1914).

    Google Scholar 

  10. L. Gruman, “The regularity of growth of entire functions, whose zeros are hyperplanes,” Ark. Matem. (Stockholm),10, No. 1, 23–31 (1972).

    Google Scholar 

  11. E. N. But, “On the entire functions of minimal growth vanishing on algebraic sets,” in: Theory of Functions, Functional Analysis, and Their Applications [in Russian], No. 20, Izd. Kharkov State Univ., Kharkov (1974), pp. 6–14.

    Google Scholar 

  12. L. I. Ronkin, “On the continuity of the indicator of an entire function ‘with plane zeros,’” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 83–85 (1980).

    Google Scholar 

  13. A. B. Sekerin, “On construction of entire functions with prescribed growth,” Sib. Mat. Zh.,27, No. 3, 179–192 (1986).

    Google Scholar 

  14. D. E. Papush, “Entire functions of several variables ‘with plane zeros,’” Dissertation, Izd. Kharkov State Univ., Kharkov (1986).

    Google Scholar 

  15. I. M. Gel'fand, M. I. Graev, and N. Ya. Vilenkin, Integral Geometry and the Problems of Representation Theory Related to It [in Russian], Nauka, Moscow (1962).

    Google Scholar 

  16. B. V. Shabat, Introduction to Complex Analysis [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  17. P. Z. Agranovich, “On functions of completely regular growth of several variables,” in: Theory of Functions, Functional Analysis, and Their Applications [in Russian], No. 30, Izd. Kharkov State Univ., Kharkov (1978), pp. 3–13.

    Google Scholar 

  18. I. M. Mysovskikh, Interpolational Cubature Formulas [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  19. L. I. Ronkin, Introduction to the Theory of Entire Functions of Several Variables [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  20. B. N. Khabibullin, “Comparison of subharmonic functions by means of their associated measures,” Mat. Sb.,125, No. 4, 522–538 (1984).

    Google Scholar 

  21. M. de Guzman, Differentiation of Integrals in Rn, Lect. Notes Math., No. 481, Springer-Verlag, Berlin-New York (1975).

    Google Scholar 

  22. L. Schwartz, Analysis [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  23. W. Rudin, Function Theory in the Unit ball of Cn, Springer-Verlag, New York-Berlin (1980).

    Google Scholar 

  24. I. Kh. Musin and A. B. Sekerin, Construction of Entire Functions with Prescribed Growth and Representation of Analytic Functions by Series in Mittag-Leffler's Functions [in Russian], dep. at VINITI on February 24, 1987, Dep. No. 1288-V87, Moscow (1987).

  25. A. B. Sekerin, On Asymptotic Approximation of Plurisubharmonic Functions [in Russian], dep. at VINITI on December 4, 1987, Dep. No. 8537-V87, Moscow (1987).

  26. V. S. Azarin, “On the functions of completely regular growth subharmonic in the entire space,” Zapiski Mekh.-Mat. Fak. Kharkov. Univ.,28, No. 4, 128–148 (1961).

    Google Scholar 

  27. L. Gruman, “Entire functions of several variables and their asymptotic growth,” Ark. Mat. (Stockholm),9, No. 1, 141–163 (1971).

    Google Scholar 

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Authors
  1. A. B. Sekerin
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Ufa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 5, pp. 142–154, September–October, 1991.

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Sekerin, A.B. Asymptotic approximation of a logarithmic potential. Sib Math J 32, 849–859 (1991). https://doi.org/10.1007/BF00971183

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  • DOI: https://doi.org/10.1007/BF00971183

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