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Phragmén-Lindelöf theorems
Author(s):
P.
C.
Fenton;
John
Rossi
Journal:
Proc. Amer. Math. Soc.
132
(2004),
761-768.
MSC (2000):
Primary 30D15
Posted:
July 28, 2003
MathSciNet review:
2019953
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Abstract:
Results of Phragmén-Lindelöf type are obtained for subharmonic functions in sectorial domains of bounded angular extent.
References:
- 1.
- Boas, R. P., Entire Functions, Academic Press, New York (1954). MR 16:914f
- 2.
- Cartwright, M. L., Integral Functions, Cambridge University Press (1956). MR 17:1067c
- 3.
- Dudley Ward, N. F. and Fenton, P. C., Some results of Phragmén-Lindelöf type, J. Math. Anal. Appl., 192 (1995), 63-70. MR 96f:30026
- 4.
- Eremenko, A., Shia, D. and Sodin, M., The minimum of the modulus of an entire function on a sequence of Pólya peaks (in Russian), Teor. Funktsii Funktsional Anal. i Prilozhen 45 (1986), 26-40. English transl. in J. Soviet Math. 48 (1990), 386-398. MR 88f:30045
- 5.
- Hayman, W. K., Subharmonic Functions, vol. 2, London Mathematical Society Monographs, No. 20, Academic Press (1989). MR 91f:31001
- 6.
- Hayman, W. K. and Kennedy, P. B., Subharmonic Functions, vol. 1, London Mathematical Society Monographs, No. 9, Academic Press (1976). MR 57:665
- 7.
- Hinkkanen, A. and Rossi, John, Entire functions with asymptotic functions, Math. Scand. 77 (1995), 153-160. MR 97j:30010
- 8.
- Rado, T., On the Problem of Plateau/Subharmonic Functions, Springer-Verlag, New York (1971). MR 49:9718
- 9.
- Tsuji, M., Potential Theory in Modern Function Theory, Maruzen Co., Tokyo (1959). MR 22:5712
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Additional Information:
P.
C.
Fenton
Affiliation:
Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand
Email:
pfenton@maths.otago.ac.nz
John
Rossi
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 26061-0123
Email:
rossi@math.vt.edu
DOI:
10.1090/S0002-9939-03-07113-2
PII:
S 0002-9939(03)07113-2
Received by editor(s):
August 28, 2002
Received by editor(s) in revised form:
October 22, 2002
Posted:
July 28, 2003
Additional Notes:
The first author completed part of this work while visiting Virginia Tech. He would like to thank the Department of Mathematics for its warm and generous hospitality and financial support.
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2003,
American Mathematical Society
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