An l1 extremal problem for polynomials

E. Beller, Bruce C. Berndt

Research output: Contribution to journalArticlepeer-review

Abstract

Let SKn be the maximum of the l1 norm, Σn|xk|, of all nth degree polynomials satisfying |Σnckzk| ≦ for |z| =1. We prove that Mn is asymptotic to √n, by exhibiting polynomials Pn (which are partial sums of certain Fourier series), whose l1 norm is asymptotic to √n.

Original languageEnglish (US)
Pages (from-to)474-481
Number of pages8
JournalProceedings of the American Mathematical Society
Volume29
Issue number3
DOIs
StatePublished - Aug 1971
Externally publishedYes

Keywords

  • Close to constant polynomials
  • Coefficients of close to constant modulus
  • Extremal polynomials
  • Partial sums of fourier series
  • U norm of polynomials
  • Upper bound for nth derivative

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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