Some properties of Faber-Walsh polynomials

Olivier Sète

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arXiv · 1306.1347

Some properties of Faber-Walsh polynomials

Olivier Sète

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Abstract

Walsh introduced a generalisation of Faber polynomials to certain compact sets which need not be connected. We derive several equivalent representations of these Faber-Walsh polynomials, analogous to representations of Faber polynomials. Some simple asymptotic properties of the Faber-Walsh polynomials on the complement of the compact set are established. We further show that suitably normalised Faber-Walsh polynomials are asymptotically optimal polynomials in the sense of [Eiermann and Niethammer 1983].

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Olivier Sète. 2013-06-06. Some properties of Faber-Walsh polynomials. https://arxiv.org/abs/1306.1347

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