Wavelets in Littlewood-Paley space, and Mexican hat completeness

H. Q. Bui, R. S. Laugesen

Research output: Contribution to journalArticle

Abstract

We resolve a long-standing question on completeness of the non-orthogonal Mexican hat wavelet system, in Lp for 1<p<2 and in the Hardy space Hp for 2/3<p≤1. Tools include the discrete Calderón condition, a generalization of the Daubechies frame criterion to a weighted L2 space, and imbeddings of that weighted space into Lp and Hardy spaces.

Original languageEnglish (US)
Pages (from-to)204-213
Number of pages10
JournalApplied and Computational Harmonic Analysis
Volume30
Issue number2
DOIs
StatePublished - Mar 1 2011

Keywords

  • Analysis
  • Frame
  • Spanning
  • Synthesis

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint Dive into the research topics of 'Wavelets in Littlewood-Paley space, and Mexican hat completeness'. Together they form a unique fingerprint.

  • Cite this