Semi-continuous and discrete wavelet frames on n-dimensional spheres

2015/04/09 by Ilona Iglewska-Nowak, I. Iglewska-Nowak · 7 citations
Mathematics · Physics and Astronomy · #Advanced Harmonic Analysis Research #Discrete wavelet transform #Holomorphic and Operator Theory #Kernel (algebra) #Legendre wavelet #Mathematical Analysis and Transform Methods #Poisson distribution #Poisson kernel #SPHERES #Wavelet #math-ph #math.CA #math.MP #msc:42C40

paper · pdf · doi:10.1016/j.acha.2015.03.010

published in Applied and Computational Harmonic Analysis 40(3), 529-552 (Elsevier BV) · 28 pages

openalex publication_date 2015/04/09 · openalex created_date 2016/06/24 · arxiv created 2018/03/05 · arxiv updated 2018/03/09 · openalex updated_date 2026/08/05

Abstract

The paper shows that under some mild conditions n-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on n-dimensional spheres constitute a discrete frame. In the proof we only use the localization properties of the reproducing kernel and its gradient.

Citations

• Poisson Wavelets on n n -Dimensional Spheres

Cited by

• Directional wavelets on n-dimensional spheres