A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem

V. Nestoridis; I. Papadoperakis

A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem

Complex Variables 2011-04-06 v1

Authors: V. Nestoridis , I. Papadoperakis

Abstract

We investigate the set of uniform limits of polynomials on any closed Jordan domain with respect to the chordal metric $\chi$ on $\mathbb{C}\cup\{\infty \}$ . We conclude that Mergelyan's Theorem may be extended to the case of uniform approximation with respect to $\chi$ on closed Jordan domains. Similar results are obtained if we replace the one point compactification $\mathbb{C}\cup\{\infty\}$ of $\mathbb{C}$ by another compactification of $\mathbb{C}$ homeomorphic to the closed unit disc.

Keywords

Mergelyan's theorem chordal metric Jordan domain uniform approximation polynomials compactification

Cite

@article{arxiv.1104.0833,
  title  = {A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem},
  author = {V. Nestoridis and I. Papadoperakis},
  journal= {arXiv preprint arXiv:1104.0833},
  year   = {2011}
}

A Remark on Two Extensions of the Disc Algebra and Mergelyan's Theorem

Abstract

Keywords

Cite

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