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Complex Approximation and Simultaneous Interpolation on Closed Sets

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier  and
W. Hengartner
P. M. Gauthier
Affiliation:
Université de Montréal, Montréal, Québec
W. Hengartner
Affiliation:
Université Laval, Québec, Québec
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Let ƒ be a complex-valued function denned on a closed subset F of the finite complex plane C, and let {Zn} be a sequence on F without limit points. We wish to find an analytic function g which simultaneously approximates ƒ uniformly on F and interpolates ƒ at the points {Zn}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 701 - 706
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Arakeljan, N. U., Approximation complexe et propriétés des fonctions analytiques, Actes Congrès intern. Math. 1970, tome 2, 595–600.Google Scholar
2. Bishop, E., Subalgebras of functions on a Riemann surface. Pacific J. Math. 8 (1958), 29–50.Google Scholar
3. Deutsch, F., Simultaneous interpolation and approximation in topological linear spaces, SIAM J. Appl. Math. H(1966), 1180–1190.Google Scholar
4. Gamelin, T. W., Uniform algebras (Prentice-Hall, Englewood Cliffs, N.J., 1969).Google Scholar
5. Gauthier, P. M. and \V. Hengartner, Uniform approximation on closed sets by functions analytic on a Riemann surface, in Approximation theory (Reidel, Dordrecht-Holland, 1975), 63–70.Google Scholar
6. Hoischen, L., Approximation and Interpolation durch ganze Funktionen, J. Approximation Theory 15 (1975), 116–123.Google Scholar
7. Nersesian, A. H., On uniform and tangential approximation by meromorphic functions, (Russian). Izv. Akad. Nauk. Arm. SSR. Ser. Mat. 7 (1972), 405–412.Google Scholar
8. Roth, A., Meromorphe approximationen, Comment. Math. Helv. 48 (1973), 151–176.Google Scholar
9. Roth, A. Uniform and tangential approximations by meromorphic functions on closed sets, Can. J. Math. 28 (1976), 104–111.Google Scholar
10. Rubel, L. A. and Venkateswaran, S., Simultaneous approximation and interpolation by entire functions, Arch. Math. 27 (1976), 526–529.Google Scholar
11. Vitushkin, A. G., Analytic capacity of sets and problems in approximation theory, Russian Math. Surveys 22 (1967), 139–200.Google Scholar