CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Author's Draft

Remarks on inner functions and optimal approximants

  • Catherine Anne Bénéteau,
    Department of Mathematics, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620-5700, USA
  • Matthew C. Fleeman,
    Baylor University, Waco, TX 76710, USA
  • Dmitry S. Khavinson,
    Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave, PHY114, Tampa, FL 33620, USA
  • Daniel Seco,
    Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
  • Alan Sola,
    Stockholm University, SE-106 91 Stockholm, Sweden
Format:   LaTeX   MathJax   PDF  

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 $1/f$, 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 inner function, reproducing Kernel Hilbert Space, operator-theoretic function theory
MSC Classifications: 46E22, 30J05 show english descriptions Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
Inner functions
46E22 - Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
30J05 - Inner functions
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/