Representations of Analytic Functions and Weihrauch Degrees

摘要

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 LPO~* shows up as the difficulty of finding the degree or the zeros.