1. CMB Online first
||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.
Keywords:inner function, reproducing Kernel Hilbert Space, operator-theoretic function theory
2. CMB 2011 (vol 56 pp. 400)