Remarks on Inner Functions and Optimal Approximants

Catherine Bénéteau, Matthew Fleeman, Dmitry Khavinson, Daniel Seco, Alan Sola

Published 2017-07-19Version 1

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.