English

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 1/f1/f, where ff 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

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

R2 v1 2026-06-22T20:51:53.935Z