Advertisement

Mathematical Notes

, Volume 57, Issue 6, pp 599–605 | Cite as

Example of a strictly linear convex domain with nonrectifiable boundary

  • S. V. Znamenskii
Article

Keywords

Convex Domain Linear Convex 
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.

References

  1. 1.
    H. Behnke and E. Peschl, “Zur Theorie der Funktionen mehrerer komplexer Veränderlichen. Konvexität in bezug auf analytische Ebenen im kleinen und großen,”Math. Ann.,111, No. 2, 158–177 (1935).MathSciNetGoogle Scholar
  2. 2.
    A. Martineau, “Sur la notion d'ensemble fortement linéelement convexe,”An. Acad. Brasil. Ciênc.,4, No. 4, 427–435 (1968).MathSciNetGoogle Scholar
  3. 3.
    S. V. Znamenskii, “Strong linear convexity,” in:Complex Analysis and Mathematical Physics, L. V. Kirenskii Physical Institute, Siberian Branch of the USSR Academy of Sciences, Krasnoyarsk (1988), pp. 39–52.Google Scholar
  4. 4.
    S. V. Znamenskii, “Tomography in spaces of analytic functionals,”Dokl. Akad. Nauk SSSR,312, No. 5, 1037–1040 (1990).MATHMathSciNetGoogle Scholar
  5. 5.
    M. Andersson and M. Passare, “Complex Kergin interpolation,”J. Approx. Theory,64, No. 2, 214–225 (1991).MathSciNetGoogle Scholar
  6. 6.
    S. V. Znamenskii, “Strong linear convexity. I. Duality in the spaces of holomorphic functions,”Sib. Mat. Zh.,26, No. 3, 32–43 (1985).MathSciNetGoogle Scholar
  7. 7.
    S. V. Znamenskii, “Geometric test for strong linear convexity,”Funkts. Anal. Prilozh.,13, No. 3, 83–84 (1979).MATHMathSciNetGoogle Scholar
  8. 8.
    Yu. B. Zelinskii, “Geometric tests for strong linear convexity,”Dokl. Akad. Nauk SSSR,261, No. 1, 11–13 (1981).MATHMathSciNetGoogle Scholar
  9. 9.
    M. Andersson, “Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform,”Bull. Soc. Math. France,120, 113–128 (1992).MATHMathSciNetGoogle Scholar
  10. 10.
    A. P. Yuzhakov and V. P. Krivokolesko, “Some properties of linearly convex domains with smooth boundaries in ℂn,”Sib. Mat. Zh., No. 2, 452–458 (1971).Google Scholar
  11. 11.
    L. Ya. Makarova, “Sufficient conditions of strong linear convexity for polyhedra,” in:Certain Problems of Multidimensional Complex Analysis, L. V. Kirenskii Physical Institute, Siberian Branch of the USSR Academy of Sciences, Krasnoyarsk (1980), pp. 89–94.Google Scholar
  12. 12.
    L. A. Aizenberg, A. P. Yuzhakov, and L. Ya. Makarova, “Linear convexity in ℂn,”Sib. Mat. Zh.,9, No. 4, 731–746 (1968).Google Scholar
  13. 13.
    Sh. A. Dautov and V. A. Stepanenko, “Simple example of a bounded domain with smooth boundary that is linear convex but nonconvex,” in:Holomorphic Functions of Several Complex Variables, L. V. Kirenskii Physical Institute, Siberian Branch of the USSR Academy of Sciences, Krasnoyarsk (1972), pp. 175–179.Google Scholar
  14. 14.
    V. A. Stepanenko, “One example of a domain with smooth boundary in ℂn that is linear convex but nonconvex,” in:On Holomorphic Functions of Several Complex Variables, L. V. Kirenskii Physical Institute, Siberian Branch of the USSR Academy of Sciences, Krasnoyarsk (1976), pp. 200–202.Google Scholar
  15. 15.
    L. A. Aizenberg, “Linear convexity in ℂn and separation of singularities of holomorphic functions,”Bull. Polish Acad. Sci. Math.,15, No. 7, 487–495 (1967).MathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • S. V. Znamenskii
    • 1
  1. 1.Krasnoyarsk State UniversityUSSR

Personalised recommendations