Remarks on Inner Functions and Optimal Approximants
Classical Analysis and ODEs
2019-08-15 v2 Complex Variables
Functional Analysis
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 , where 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.
Cite
@article{arxiv.1707.06166,
title = {Remarks on Inner Functions and Optimal Approximants},
author = {Catherine Bénéteau and Matthew Fleeman and Dmitry Khavinson and Daniel Seco and Alan Sola},
journal= {arXiv preprint arXiv:1707.06166},
year = {2019}
}
Comments
17 pages, fixed typos