Uniqueness and non uniqueness for harmonic functions with zero nontangential limits

  • J. Marshall Ash
  • Russell Brown
Conference paper


Definitions. By D we mean the open unit disc which is centered at the origin in the complex plane and by Twe mean its boundary, i.e., its circumference.


Harmonic Function Trigonometric Series Subharmonic Function Open Unit Disc Radial Limit 


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  1. [BN]
    J. Bak and D.J. Newman, Complex Analysis, Springer, New York, 1982.MATHGoogle Scholar
  2. [D]
    B. E. J. Dahlberg, On the radial boundary values of subharmonic functions, Math. Scand. 40(1977), 301–317.MathSciNetMATHGoogle Scholar
  3. [De]
    N.G. DeBruijn, Asymptotic Methods in Analysis, Dover, New York, 1981.Google Scholar
  4. [FS]
    C. Fefferman and E. M. Stein, H pspaces of several variables, Acta Math. 129 (1972), 137–192.MathSciNetMATHGoogle Scholar
  5. [R]
    W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1987.MATHGoogle Scholar
  6. [S]
    V. Shapiro, The uniqueness of functions harmonic in the interior of the unit disk, Proc. Lond. Math. Soc. 13(1963), 639–652.MATHCrossRefGoogle Scholar
  7. [T]
    M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959.MATHGoogle Scholar
  8. [V]
    S. Verblunsky, On the theory of trigonometric series, (I) Proc. Lond. Math. Soc. 34(1932), 441–456CrossRefGoogle Scholar
  9. S. Verblunsky, On the theory of trigonometric series, (II) Proc. Lond. Math. Soc. 34(1932) 457–491.MATHCrossRefGoogle Scholar
  10. [W]
    F. Wolf, The Poisson integral. A study in the uniqueness of harmonic functions, Acta Math. 74(1941), 65–100.MathSciNetCrossRefGoogle Scholar
  11. [Z]
    A. Zygmund, Trigonometric Series, Vols.I, II, Cambridge Univ. Press, Cambridge, 1959.MATHGoogle Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • J. Marshall Ash
    • 1
  • Russell Brown
    • 2
  1. 1.DePaul UniversityChicagoUSA
  2. 2.University of KentuckyLexingtonUSA

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