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Radial limits of harmonic functions on the unit disc
Author(s):
Stephen
J.
Gardiner
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1387-1389.
MSC (2000):
Primary 31A20;
Secondary 41A30
Posted:
November 1, 2004
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Abstract:
This note characterizes those functions on the unit circle that can arise as the radial limit function of a harmonic function on the unit disc.
References:
- 1.
- D. H. Armitage and S. J. Gardiner, Classical Potential Theory, Springer, London, 2001. MR 1801253 (2001m:31001)
- 2.
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- 3.
- A. Boivin and P. V. Paramonov, On radial limit functions for entire solutions of second order elliptic equations in
 , Publ. Mat. 42 (1998), 509-519. MR 1676041 (99m:35043) - 4.
- D. Gaier, Lectures on Complex Approximation, Birkh äuser, Boston, 1987.MR 0894920 (88i:30059b)
- 5.
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- 6.
- L. L. Helms, Introduction to Potential Theory, Krieger, New York 1975.MR 0460666 (57:659)
- 7.
- L. H. Loomis, The converse of the Fatou theorem for positive harmonic functions, Trans. Amer. Math. Soc. 53 (1943), 239-250. MR 0007832 (4:199d)
- 8.
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Additional Information:
Stephen
J.
Gardiner
Affiliation:
Department of Mathematics, University College Dublin, Dublin 4, Ireland
Email:
stephen.gardiner@ucd.ie
DOI:
10.1090/S0002-9939-04-07734-2
PII:
S 0002-9939(04)07734-2
Received by editor(s):
January 2, 2004
Posted:
November 1, 2004
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2004,
American Mathematical Society
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