2014/10/08 by Ilona Iglewska-Nowak · 2 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Fourier analysis #Legendre wavelet #Limit (mathematics) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Poisson distribution #SPHERES #Shearlet #Space (punctuation) #Wavelet #math-ph #math.CA #math.MP #msc:42C40
paper · pdf · doi:10.1007/s00041-014-9366-x
published as J. Fourier Anal. Appl. 21 (2015), no. 1, 206-227 · 17 pages
openalex publication_date 2014/10/08 · arxiv created 2018/03/05 · arxiv updated 2018/03/09 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
In this paper, Poisson wavelets on n-dimensional spheres, derived from Poisson kernel, are introduced and characterized. We compute their Gegenbauer expansion with respect to the origin of the sphere, as well as with respect to the field source. Further, we give recursive formulae for their explicit representations and we show how the wavelets are localized in space. Also their Euclidean limit is calculated explicitly and its space localization is described. We show that Poisson wavelets can be treated as wavelets derived from approximate identities and we give two inversion formulae.