Polynomial extremal problems in lp

E. B. Beller

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


For p»2, letmp, n be the minimum of the Lp norm all nth degree polynomials Σnakeikt ateikt which satisfy |ak| =1, k = 0, 1, ···, n. We exhibit certain polynomials Pn whose Lp norm(2<p<∞) is asymptotic to √n, thereby proving that mp, n is itself asymptotic to √n. We also show that the sup norm of (essentially) the same polynomials isasymptotic to (1.1716 …)X√n.

Original languageEnglish
Pages (from-to)249-259
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Oct 1971
Externally publishedYes


  • Close to constant polynomials
  • Coefficients of constant modulus
  • Extremal polynomials
  • Fresnel integral
  • L norms of polynomials
  • Sup norm of polynomials
  • Van der corput's lemma


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