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International Computer Science Symposium in Russia

CSR 2016: Computer Science – Theory and Applications pp 367–381Cite as

Representations of Analytic Functions and Weihrauch Degrees

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9691))

Abstract

This paper considers several representations of the analytic functions on the unit disk and their mutual translations. All translations that are not already computable are shown to be Weihrauch equivalent to closed choice on the natural numbers. Subsequently some similar considerations are carried out for representations of polynomials. In this case in addition to closed choice the Weihrauch degree \(\text {LPO}^*\) shows up as the difficulty of finding the degree or the zeros.

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Acknowledgements

The work has benefited from the Marie Curie International Research Staff Exchange Scheme Computable Analysis, PIRSES-GA-2011- 294962. The first author was supported partially by the ERC inVEST (279499) project, the second by the International Research Training Group 1529 ‘Mathematical Fluid Dynamics’ funded by the DFG and JSPS.

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Cambridge, UK

    Arno Pauly

  2. Département d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Arno Pauly

  3. Fachbereich Mathematik, TU-Darmstadt, Darmstadt, Germany

    Florian Steinberg

Authors
  1. Arno Pauly
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  2. Florian Steinberg
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Correspondence to Arno Pauly .

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Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

  2. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Pauly, A., Steinberg, F. (2016). Representations of Analytic Functions and Weihrauch Degrees. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_26

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  • DOI: https://doi.org/10.1007/978-3-319-34171-2_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34170-5

  • Online ISBN: 978-3-319-34171-2

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