Remarks on Inner Functions and Optimal Approximants
  We discuss the concept of inner function in reproducing kernel Hilbert spaces
with an orthogonal basis of monomials and examine connections between inner
functions and optimal polynomial approximants to $1/f$, where $f$ is a function
in the space. We revisit some classical examples from this perspective, and
show how a construction of Shapiro and Shields can be modified to produce inner
functions.
