Representations of Analytic Functions and Weihrauch Degrees

  • Arno PaulyEmail author
  • Florian Steinberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)


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.


Computable analysis Analytic function Weihrauch reduction Polynomials Closed choice LPO* 



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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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK
  2. 2.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  3. 3.Fachbereich MathematikTU-DarmstadtDarmstadtGermany

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