Harmonic functions having no tangential limits
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- by Hiroaki Aikawa
- Proc. Amer. Math. Soc. 108 (1990), 457-464
- DOI: https://doi.org/10.1090/S0002-9939-1990-0990410-X
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Abstract:
Let ${C_0}$ be a tangential curve in $D = \left \{ {|z| < 1} \right \}$ which ends at 1 and let ${C_\theta }$ be its rotation about the origin through an angle $\theta$. We construct a bounded harmonic function in $D$ which fails to have limits along ${C_\theta }$ for all $\theta ,0 \leq \theta \leq 2\pi$.References
- David A. Brannan and James G. Clunie (eds.), Aspects of contemporary complex analysis, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. MR 623462
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999 J. E. Littlewood, On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172-176.
- A. J. Lohwater and G. Piranian, The boundary behavior of functions analytic in a disk, Ann. Acad. Sci. Fenn. Ser. A. I. 1957 (1957), no. 239, 17. MR 91342
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 457-464
- MSC: Primary 31A20; Secondary 30D40, 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1990-0990410-X
- MathSciNet review: 990410