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Uniform And Tangential Approximations By Meromorphic Functions on Closed Sets

Published online by Cambridge University Press:  20 November 2018

Alice Roth
Alice Roth*
Affiliation:
Willadingweg 34, CH-3006 Berne, Switzerland
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Let G be an (open) domain in the finite complex plane and F a relatively closed proper subset of G. We denote by M(G) the set of functions meromorphic on G and as usual by R(K) (for a compact set K) the set of uniform limits of rational functions without poles on K.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 104 - 111
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Arakeljan, N. U., Approximations complexe et propriétés des fonctions analytiques, Actes Congrès Intern. Math., 2 (1970), 595–600.Google Scholar
2. Brown, L. and Gauthier, P. M., The local range set of a meromorphic function, Proc. Amer. Math. Soc. 41 (1973), 518–524.Google Scholar
3. Mergeljan, S. N., Uniform approximations to functions of a complex variable, Amer. Math. Soc. Translations, 3, p. 294–391.Google Scholar
4. Nersesian, A. H., On uniform and tangential approximation by meromorphic functions (Russian), Izv. Akad. Nauk. Arm. SSR, Ser. Math. VII, No. 6 (1972), 405–412.Google Scholar
5. Roth, Alice, Approximationseigenschaften und Strahlengrenzwerte meromorpher und ganzer Funktionen, Comment. Math. Helv., 11 (1938), 77–125.Google Scholar
6. Roth, Alice, Meromorphe Approximationen, Comment. Math. Helv. J+8 (1973), 151–176.Google Scholar
7. Zalcman, L., Analytic capacity and rational approximation (Springer-Verlag Berlin, Heidelberg, New York, 1968).Google Scholar