Title: Remarks on Inner Functions and Optimal Approximants,
Abstract: 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.