Advertisement

Arkiv för Matematik

, Volume 18, Issue 1–2, pp 53–72 | Cite as

Positive harmonic functions vanishing on the boundary of certain domains inR n

  • Michael Benedicks
Article

Keywords

Dirichlet Problem Harmonic Measure Maximum Modulus Subharmonic Function Martin Boundary 
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.
    Ancona, A., Une propriété de la compactification de Martin d’un domaine euclidien,Ann. Inst. Fourier (Grenoble) 29 (1979), 71–90.MATHMathSciNetGoogle Scholar
  2. 2.
    Benedicks, M., Positive harmonic functions vanishing on the boundary of certain domains inR n+1,Proceedings of Symposia in Pure Mathematics Vol. XXXV, Part 1 (1979), 345–348.MathSciNetGoogle Scholar
  3. 3.
    Boas, R. P., Jr.,Entire functions, Academic Press, New York, 1954.MATHGoogle Scholar
  4. 4.
    Domar, Y., On the existence of a largest subharmonic minorant of a given function,Ark. Mat. 3 (1957), 429–440.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Friedland, S. &Hayman, W. K., Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions,Comm. Math. Helv. 51 (1976), 133–161.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hayman, W. K., On the domains where a harmonic or subharmonic function is positive,Advances in complex function theory, Lecture Notes in Mathematics 505, Springer-Verlag, Berlin, 1974.Google Scholar
  7. 7.
    Hayman, W. K. &Ortiz, E. L., An upper bound for the largest zero of Hermite’s function with applications to subharmonic functions,Proc. Royal Soc. Edinburgh 17 (1975/76), 183–197.Google Scholar
  8. 8.
    Helms, L. L.,Introduction to potential theory, Wiley, New York, 1969.MATHGoogle Scholar
  9. 9.
    Kesten, H., Positive harmonic functions with zero boundary values,Proceedings of Symposia in Pure Mathematics Vol. XXXV, Part 1 (1979), 349–352.MathSciNetGoogle Scholar
  10. 10.
    Kesten, H., Positive harmonic functions with zero boundary values. Preprint.Google Scholar
  11. 11.
    Kjellberg, B.,On certain integral and harmonic functions, Thesis, Uppsala, 1948.Google Scholar
  12. 12.
    Kjellberg, B., On the growth of minimal positive harmonic functions in a plane domain,Ark. Mat. 1 (1951), 347–351.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kjellberg, B., Problem 3.12,Symposium on complex analysis Canterbury, 1973, 163. Cambridge University Press (1974).Google Scholar
  14. 14.
    Levinson, N.,Gap and density theorems, American Math. Soc. Col. Publ. Vol. XXVI.Google Scholar

Copyright information

© Institut Mittag-Leffler 1980

Authors and Affiliations

  • Michael Benedicks
    • 1
  1. 1.Institut Mittag-LefflerDjursholmSweden

Personalised recommendations