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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

1. Ahlfors, L., Riemann surfaces and extremal problems on compact subregions, Comment. Math. Helv. 8 (1950), 100–134.Google Scholar
2. de Leeuw, K. and Rudin, W., Extreme points and extremum problems in H\ Pacific J. Math. 8 (1958), 467–485.Google Scholar
3. Forelli, F., Extreme points in Hl(R), Can. J. Math. 19 (1967), 312–320.Google Scholar
4. Hoffman, K., Banach spaces of analytic functions (Prentice-Hall, Englewood Cliffs, N.J., 1962).Google Scholar
5. Royden, H., The Riemann-Roch theorem, Comment. Math. Helv. 84 (1960), 37–51.Google Scholar
6. Royden, H., The boundary values of analytic and harmonic functions, Math. Z. 78 (1962), 1–24.Google Scholar
7. Springer, G., Introduction to Riemann Surfaces (Addison-Wesley, Reading, Mass., 1957).Google Scholar
8. Voichick, M., Ideals and invariant subspaces of analytic functions, Trans. Amer. Math. Soc. 13 (1964), 493–512.Google Scholar
9. Voichick, M. and Zalcman, L., Inner and outer functions on Riemann surfaces, Proc. Amer. Math. Soc. 16 (1965), 1200–1204.Google Scholar