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The Phragmén-Lindelöf Principle

Published online by Cambridge University Press:  20 November 2018

Michael D. Humphries
Michael D. Humphries*
Affiliation:
Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri 65401, U.S.A.
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The theorem below is one version of the Phragmén-Lindelöf principle [4], which extends the maximum modulus theorem. The theorem has many applications, including the proof of a better-known but less general result [3], which is sometimes attributed to Phragmén and Lindelöf.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 121
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Conway, John B., Functions of One Complex Variable, 2nd Edition, Springer-Verlag, New York, 1978.Google Scholar
2. Hille, Einar, Analytic Function Theory, Vol. II, Ginn, New York, 1962.Google Scholar
3. Phragmén, E., Sur une extension d'un théorème classique de la théorie des fonctions, Acta Math., 28 (1962), 351-368.Google Scholar
4. Phragmén, E. and Lindelôf, Ernst, Sur une extension d'un principe classique de l'analyse, Acta Math., 31 (1962), 381-406.Google Scholar