Convergence in Hausdorff Content of Pade-Faber Approximants and Its Applications

Nattapong Bosuwan, Waraporn Chonlapap

Abstract


A convergence in Hausdorff content of Pade-Faber approximants (recently introduced) on some certain sequences is proved. As applications of this result, we give an alternate proof of a Montessus de Ballore type theorem for these  Pade-Faber approximants and a proof of a convergence of Pade-Faber approximants in the maximal canonical domain in which the approximated function can be continued to a meromorphic function.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|