Multiresolution on n-dimensional spheres
Classical Analysis and ODEs
2018-04-10 v1 Mathematical Physics
math.MP
Abstract
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are examined. Decomposition and reconstruction algorithms for the wavelet transform are presented. Formulae for variances in space and momentum domain, as well as for the uncertainty product, of zonal functions over n-dimensional spheres are derived and applied to the scaling functions.
Cite
@article{arxiv.1804.03043,
title = {Multiresolution on n-dimensional spheres},
author = {Ilona Iglewska-Nowak},
journal= {arXiv preprint arXiv:1804.03043},
year = {2018}
}
Comments
24 pages