Divergent Jacobi polynomial series

Christopher Meaney

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Fix real numbers α ≥ β ≥ - 1/2, with α > - 1/2, and equip [-1, 1] with the measure dμ(x) = (1 - x)α(1 + x)β dx. For p = 4(α + l)/(2α + 3) there exists f ∈ Lp(μ) such that f(x) = 0 a.e. on [-1, 0] and the appropriate Jacobi polynomial series for f diverges a.e. on [-1.1] This implies failure of localization for spherical harmonic expansions of elements of L2d/(d+1)(X), where X is a sphere or projective space of dimension d > 1.

Original languageEnglish
Pages (from-to)459-462
Number of pages4
JournalProceedings of the American Mathematical Society
Volume87
Issue number3
DOIs
Publication statusPublished - 1983
Externally publishedYes

    Fingerprint

Keywords

  • Compact two-point homogeneous space
  • Jacobi polynomial
  • Laplace-Beltrami operator
  • Localization
  • Spherical harmonic
  • Zonal

Cite this