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Possibility of Uniform Rational Approximation in the Spherical Metric

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier ,
A. Roth  and
J. L. Walsh
P. M. Gauthier
Affiliation:
Université de Montréal, Montréal, Québec
A. Roth
Affiliation:
Université de Montréal, Montréal, Québec
J. L. Walsh
Affiliation:
Willadingweg 34, CH 3006 Berne, Switzerland
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Let ƒ b e a mapping defined on a compact subset K of the finite complex plane C and taking its values on the extended plane C ⋃ ﹛ ∞﹜. For x a metric on the extended plane, we consider the possibility of approximating ƒ x-uniformly on K by rational functions. Since all metrics on C ⋃ ﹛oo ﹜ are equivalent, we shall consider that x is the chordal metric on the Riemann sphere of diameter one resting on a finite plane at the origin.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 112 - 115
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Behnke, H. and Thullen, P., Théorie der funktionen mehrerer komplexer verdnderlichen, edited by Remmert, R. (Springer-Verlag. New York, 1970).Google Scholar
2. Roth, A., Uniform and tangential approximation by meromorphic functions on closed sets, Can. J. Math, (to appear).Google Scholar
3. Zalcman, L., Analytic capacity and rational approximation, Springer Lecture Notes 50 (Springer-Verlag. New York, 1968).Google Scholar