Remarks on Inner Functions and Optimal Approximants
Catherine Bénéteau, Matthew Fleeman, Dmitry Khavinson, Daniel Seco, Alan A. Sola · Canadian Mathematical Bulletin · 2017
Abstract We discuss the concept of inner function in reproducing kernelHilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to 1/f, wherefis a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modiûed to produce inner functions.