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Extreme Points in Spaces of Analytic Functions

Published online by Cambridge University Press:  20 November 2018

T. W. Gamelin  and
M. Voichick
T. W. Gamelin
Affiliation:
M.I.T., Cambridge, Massachusetts, Universidad Nacional de La Plata, La Plata, Argentina; University of Wisconsin, Madison, Wisconsin
M. Voichick
Affiliation:
M.I.T., Cambridge, Massachusetts, Universidad Nacional de La Plata, La Plata, Argentina; University of Wisconsin, Madison, Wisconsin
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Our aim in this paper is to obtain some theorems concerning spaces of analytic functions on a finite open Riemann surface R which extend known results for the disc △ = {|z| < 1}. Suppose that R has a smooth boundary bR consisting of t closed curves, and that the interior genus of R is s. The first Betti number of R is then r = 2s + t — 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 919 - 928
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

The work of the second author was supported by the NSF grant GP-3483.

References

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