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Uniform And Tangential Approximations By Meromorphic Functions on Closed Sets

  • Alice Roth (a1)
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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.

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References
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1. Arakeljan, N. U., Approximations complexe et propriétés des fonctions analytiques, Actes Congrès Intern. Math., 2 (1970), 595600.
2. Brown, L. and Gauthier, P. M., The local range set of a meromorphic function, Proc. Amer. Math. Soc. 41 (1973), 518524.
3. Mergeljan, S. N., Uniform approximations to functions of a complex variable, Amer. Math. Soc. Translations, 3, p. 294391.
4. Nersesian, A. H., On uniform and tangential approximation by meromorphic functions (Russian), Izv. Akad. Nauk. Arm. SSR, Ser. Math. VII, No. 6 (1972), 405412.
5. Roth, Alice, Approximationseigenschaften und Strahlengrenzwerte meromorpher und ganzer Funktionen, Comment. Math. Helv., 11 (1938), 77125.
6. Roth, Alice, Meromorphe Approximationen, Comment. Math. Helv. J+8 (1973), 151176.
7. Zalcman, L., Analytic capacity and rational approximation (Springer-Verlag Berlin, Heidelberg, New York, 1968).
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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