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Simultaneous Approximation and Interpolation on Arakelian Sets

Published online by Cambridge University Press:  20 November 2018

Nikolai Nikolov  and
Peter Pflug
Nikolai Nikolov
Affiliation:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria e-mail: nik@math.bas.bg
Peter Pflug
Affiliation:
Carl von Ossietzky Universität Oldenburg, Institut für Mathematik, Postfach 2503, D-26111 Oldenburg, Germany e-mail: pflug@mathematik.uni-oldenburg.de
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Abstract

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We extend results of P. M. Gauthier, W. Hengartner and A. A. Nersesyan on simultaneous approximation and interpolation on Arakelian sets.

Keywords

30E10Arakelian's theoremArakelian sets
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 1 , 01 March 2007 , pp. 123 - 125
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] Arakelian, N. U., Uniform and tangential approximations by analytic functions. Amer. Math. Soc. Transl. (2), 122(1984), 85–97.Google Scholar
[2] Gauthier, P. M. and Hengartner, W., Complex approximation and simultaneous interpolation on closed sets. Canad. J. Math. 29(1977), no. 4, 701–706.Google Scholar
[3] Nersesyan, A. A., Uniform approximation with simultaneous interpolation by analytic functions. Izv. Akad. Nauk Armyan SSR Ser. Mat. 15(1980), no. 4, 249–257.Google Scholar
[4] Nikolov, N. and Pflug, P., The multipole Lempert function is monotone under inclusion of pole sets. Michigan Math. J. 54(2006), 111–116.Google Scholar