Prony's method on the sphere
Numerical Analysis
2016-03-08 v1 Algebraic Geometry
Abstract
Eigenvalue analysis based methods are well suited for the reconstruction of finitely supported measures from their moments up to a certain degree. We give a precise description when Prony's method succeeds in terms of an interpolation condition. In particular, this allows for the unique reconstruction of a measure from its trigonometric moments whenever its support is separated and also for the reconstruction of a measure on the unit sphere from its moments with respect to spherical harmonics. Both results hold in arbitrary dimensions and also yield a certificate for popular semidefinite relaxations of these reconstruction problems.
Keywords
Cite
@article{arxiv.1603.02020,
title = {Prony's method on the sphere},
author = {Stefan Kunis and H. Michael Möller and Ulrich von der Ohe},
journal= {arXiv preprint arXiv:1603.02020},
year = {2016}
}