  This paper compares different representations (in the sense of computable
analysis) of a number of function spaces that are of interest in analysis. In
particular subspace representations inherited from a larger function space are
compared to more natural representations for these spaces. The formal framework
for the comparisons is provided by Weihrauch reducibility.
  The centrepiece of the 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. As a final example, the smooth
functions are contrasted with functions with bounded support and Schwartz
functions. Here closed choice on the natural numbers and the lim degree appear.
