Completeness of the Grid Translates of Functions

Swagato K. Ray, Rudra P. Sarkar, Yitzhak Weit

Research output: Contribution to journalArticlepeer-review

Abstract

If f ∈ Lp(ℝd) is a bounded real valued continuous function which has a unique maximum or a unique minimum at a point x0 ∈ ℝd and if the inverse image of the neighborhoods of f(x 0) shrinks regularly to x 0, then span (Formula Presented) is a dense subset of Lp(ℝd), 1 ≤ p< ∞ where f m(x)=f(x)m and {e i} is the natural basis of Rd. The result extends to all homogeneous groups, Riemannian symmetric spaces of noncompact type, Damek-Ricci spaces etc.

Original languageEnglish
Pages (from-to)186-198
Number of pages13
JournalJournal of Fourier Analysis and Applications
Volume20
Issue number1
DOIs
StatePublished - Feb 2014

Keywords

  • Euclidean space
  • Grid-translate
  • Homogeneous group
  • Riemannian symmetric space

ASJC Scopus subject areas

  • Analysis
  • Mathematics (all)
  • Applied Mathematics

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