Böttcher, Albrecht ; Kunis, Stefan ; Potts, Daniel : Probabilistic Spherical Marcinkiewicz-Zygmund Inequalities

Author(s):

Böttcher, Albrecht
Kunis, Stefan
Potts, Daniel

Title:

Probabilistic Spherical Marcinkiewicz-Zygmund Inequalities

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 21, 2007

Mathematics Subject Classification:

41A17			[ Inequalities in approximation ]
33C55			[ Spherical harmonics ]
60H30			[ Applications of stochastic analysis ]
15A60			[ Norms of matrices, numerical range, applications of functional analysis to matrix theory ]

Abstract:

Recently, norm equivalences between spherical polynomials and their sample values at scattered sites have been proved. These so-called Marcinkiewicz-Zygmund inequalities involve a parameter that characterizes the density of the sampling set and they are applicable to all polynomials whose degree does not exceed an upper bound that is determined by the density parameter. We show that if one is satisfied by norm equivalences that hold with prescribed probability only, then the upper bound for the degree of the admissible polynomials can be enlarged significantly and that then, moreover, there exist fixed sampling sets which work for polynomials of all degrees.

Keywords:

Scattered data, Marcinkiewicz-Zygmund inequalities, Spherical harmonics, Random polynomials

Language:

English

Publication time:

10 / 2007