Zeros of optimal polynomial approximants in Articles uri icon


  • Cheng, Raymond
  • Ross, William T.

publication date

  • August 2022

start page

  • 1

end page

  • 39


  • 108396


  • 404, Part A

International Standard Serial Number (ISSN)

  • 0001-8708

Electronic International Standard Serial Number (EISSN)

  • 1090-2082


  • The study of inner and cyclic functions in (fórmula) spaces requires a better understanding of the zeros of the so-called optimal polynomial approximants. We determine that a point of the complex plane is the zero of an optimal polynomial approximant for some element of (fórmula) if and only if it lies outside of a closed disk (centered at the origin) of a particular radius which depends on the value of p. We find the value of this radius for (fórmula). In addition, for each positive integer d there is a polynomial (fórmula) of degree at most d that minimizes the modulus of the root of its optimal linear polynomial approximant. We develop a method for finding these extremal functions (fórmula) and discuss their properties. The method involves the Lagrange multiplier method and a resulting dynamical system.


  • Computer Science
  • Mathematics
  • Statistics


  • banach spaces; cyclic functions; inner functions; optimal polynomial approximants; sequence spaces