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Extreme Points in H1(R)

Published online by Cambridge University Press:  20 November 2018

Frank Forelli
Frank Forelli*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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Let R be an open Riemann surface. ƒ belongs to H1(R) if ƒ is holomorphic on R and if the subharmonic function |ƒ| has a harmonie majorant on R. Let p be in R and define ||ƒ|| to be the value at p of the least harmonic majorant of |ƒ|. ||ƒ|| is a norm on the linear space H1(R), and with this norm H1(R) is a Banach space (7). The unit ball of H1(R) is the closed convex set of all ƒ in H1(R) with ||ƒ|| ⩽ 1. Problem: What are the extreme points of the unit ball of H1(R)? de Leeuw and Rudin have given a complete solution to this problem where R is the open unit disk (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 312 - 320
Copyright
Copyright © Canadian Mathematical Society 1967

References

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