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Small subharmonic functions

Published online by Cambridge University Press:  17 April 2009

P.C. Fenton
P.C. Fenton
Affiliation:
Department of Mathematics, University of Otago, Box 56, Dunedin, New Zealand.
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Abstract

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Some time ago Barry [Proc. London Math. Soc. 12 (1962), 445–495] established the right connection between the smallest and largest values of small subharmonic functions on certain circles about the origin. The behaviour of functions extremal for this connection is investigated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1984 , pp. 67 - 82
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Barry, P.D., “The minimum modulus of small integral and subharmonic functions”, Proc. London Math. Soc. (3) 12 (1962), 445–495.CrossRefGoogle Scholar
[2]Boas, Ralph Philip Jr, Entire functions (Pure and Applied Mathematic Mathematics, 5. Academic Press, New York, 1954).Google Scholar
[3]Fenton, P.C., “Regularity of certain small subharmonic functions”, Trans. Amer. Math. Soc. 262 (1980), 473–486.CrossRefGoogle Scholar
[4]Fenton, P.C., “The infimum of small subharmonic functions”, Proc. Amer. Math. Soc. 78 (1980), 43–47.Google Scholar
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[6]Kjellberg, Bo, “A theorem on the minimum modulus of entire functions”, Math. Scand. 12 (1963), 5–11.Google Scholar