Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-04T10:15:41.503Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform Approximation by Meromorphic Functions on Closed Sets with Continuous extension into the Boundary

Published online by Cambridge University Press:  20 November 2018

Alice Roth
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Notation. For S a subset of the extended plane C* = C ∪ (∞ ) let S0 be its interior, its closure in C* and its boundary. H(S) and M(S) will denote the sets of all restrictions to S of functions which are, on a neighborhood of S, holomorphic or meromorphic, respectively. A (S) will stand for the set of functions from S to C* which are continuous on S and whose restriction to S° are holomorphic.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1243 - 1255
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Arakeljan, N. U., Approximations complexes et propriétés des fonctions analytiques, Actes du 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, 294–391.Google Scholar
4. Nersesian, A. H., On uniform and tangential approximation by meromorphic functions (Russian). Izv. Akad. Nauk Armen. SSR., Ser. Math. VII 6 (1972), 405–412.Google Scholar
5. Roth, Alice, Approximationseigenschaften und Strahlengrenzwerte meromorpher und ganzcr Funktionen, Comment. Math. Helv. 11 (1938), 77–125.Google Scholar
6. Roth, Alice Meromorphe Approximationen, Comment. Math. Helv. 48 (1973), 151–176.Google Scholar
7. Roth, Alice Uniform and tangential approximations by meromorphic functions on closed sets, Can. J. Math. 28 (1976), 104–111.Google Scholar
8. Stray, A., On uniform and asymptotic approximation, to appear.Google Scholar