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Approximation by random complex polynomials and random rational functions

Volume 123 / 2019

Paul M. Gauthier, Thomas Ransford, Simon St-Amant, Jérémie Turcotte Annales Polonici Mathematici 123 (2019), 267-294 MSC: Primary 30E10, 32E20; Secondary 30H50, 28A20. DOI: 10.4064/ap180912-20-2 Published online: 27 May 2019

Abstract

We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness can be used to ‘improve’ convergence for sequences of functions.

Authors

  • Paul M. GauthierDépartement de Mathématiques et de Statistique
    Université de Montréal
    CP-6128 Centreville
    Montréal, H3C 3J7, Canada
    e-mail
  • Thomas RansfordDépartement de Mathématiques et de Statistique
    Université Laval
    Québec G1V 0A6, Canada
    e-mail
  • Simon St-AmantDépartement de Mathématiques et de Statistique
    Université de Montréal
    CP-6128 Centreville
    Montréal, H3C 3J7, Canada
    e-mail
  • Jérémie TurcotteDépartement de Mathématiques et de Statistique
    Université de Montréal
    CP-6128 Centreville
    Montréal, H3C 3J7, Canada
    e-mail

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