Advertisement

Siberian Mathematical Journal

, Volume 27, Issue 6, pp 825–837 | Cite as

Univalent functions and regularly measurable maps

  • A. Z. Grinshpan
Article

Keywords

Univalent Function 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    S. L. Krushkal' and R. Kühnau, Quasiconformal Mappings: New Methods and Applications [in Russian], Nauka, Novosibirsk (1984).Google Scholar
  2. 2.
    A. Z. Grinshpan, “Growth of coefficients of univalent functions with quasiconformal extension,” Sib. Mat. Zh.,23, No. 2, 208–211 (1982).Google Scholar
  3. 3.
    A. Z. Grinshpan, “Coefficient inequalities for conformal mappings with homeomorphic extension,” Sib. Mat. Zh.,26, No. 1, 49–65 (1985).Google Scholar
  4. 4.
    L. de Branges, “A proof of the Bieberbach conjeccture,” Acta Math.,154, 137–152 (1985).Google Scholar
  5. 5.
    M. Schiffer and G. Schober, “Coefficient problems and generalized Grunsky inequalities for schlicht functions with quasiconformal extensions,” Arch. Ration. Mech. Anal.,60, No. 3, 205–228 (1976).Google Scholar
  6. 6.
    V. Ya. Gutlyanskii and V. A. Shchepetev, “Sharp estimates of the modulus of a univalent analytic function with quasiconformal extension,” Mat. Zametki,33, No. 2, 179–186 (1983).Google Scholar
  7. 7.
    G. D. Suvorov, Families of Planar Topological Maps [in Russian], Nauka, Novosibirsk (1965).Google Scholar
  8. 8.
    M. Milin, Univalent Functions and Orthonormal Systems [in Russian], Nauka, Moscow (1971).Google Scholar
  9. 9.
    G. H. Fitzgerald, “Quadratic inequalities and coefficient estimates for schlicht functions,” Arch. Ration. Mech. Anal.,46, No. 5, 356–368 (1972).Google Scholar
  10. 10.
    N. A. Lebedev, Area Principle in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1975).Google Scholar
  11. 11.
    V. Ya. Gutlyanskii, “Area principle for a class of quasiconformal maps,” Dokl. Akad. Nauk SSSR,212, No. 3, 540–543 (1973).Google Scholar
  12. 12.
    L. Ahlfors, Lectures on Quasiconformal Mappins [Russian translation], Mir, Moscow (1969).Google Scholar
  13. 13.
    V. G. Sheretov, “A version of the area theorem,” in: Mathematical Analysis [in Russian], Izd-vo Kubanskogo Un-ta, Krasnodar, Vol. 217, No. 3 (1976), pp. 77–80.Google Scholar
  14. 14.
    S. L. Sobolev, Applications of Functional Analysis to Mathematical Physics [in Russian], Leningrad State Univ. (1959).Google Scholar
  15. 15.
    Chr. Pommerenke, Univalent Functions, Verlag Vandenhoeck und Ruprecht, Göttingen (1975).Google Scholar
  16. 16.
    P. L. Duren, Univalent Functions, Springer-Verlag, New York (1983).Google Scholar
  17. 17.
    R. Kühnau, “Quasikonforme Fortsetzbarkeit, Fredholmsche Eigenwerte und Grunskysche Koeffizientenbedingungen,” Ann. Acad. Fenn., S. A. I. Math.,7, 383–391 (1982).Google Scholar
  18. 18.
    V. I. Smirnov and N. A. Lebedev, Constructive Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1964).Google Scholar
  19. 19.
    A. Z. Grinshpan, “Degree stability for Bieberbach's inequality,” J. Sov. Math.,26, No. 6 (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • A. Z. Grinshpan

There are no affiliations available

Personalised recommendations