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Taylor Series, Universality and Potential Theory

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New Trends in Approximation Theory

Part of the book series: Fields Institute Communications ((FIC,volume 81))

Abstract

Universal approximation properties of Taylor series have been intensively studied over the past 20 years. This article highlights the role that potential theory has played in such investigations. It also briefly discusses potential theoretic aspects of universal Laurent series, universal Dirichlet series, and universal polynomial expansions of harmonic functions.

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Acknowledgements

The author is grateful to the referee for a careful reading of the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland

    Stephen J. Gardiner

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  1. Stephen J. Gardiner
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Correspondence to Stephen J. Gardiner .

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Editors and Affiliations

  1. Département de Mathématiques et de Statistique, Université Laval, Québec, Québec, Canada

    Javad Mashreghi

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, USA

    Myrto Manolaki

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montreal, Québec, Canada

    Paul Gauthier

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Gardiner, S.J. (2018). Taylor Series, Universality and Potential Theory. In: Mashreghi, J., Manolaki, M., Gauthier, P. (eds) New Trends in Approximation Theory. Fields Institute Communications, vol 81. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7543-3_14

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