Theory and applications of a functional from metric geometry

For positive α, and for complex measures μ and $\nu$ on R$\sp{n}$, define J\spα(μ,\nu)=\int\int\vert x-y\vert\spα dμ(x)d\bar \nu(y). Study of the energy integral J\spα has its roots in metric embedding theory and potential theory. Subject to certain moment vanishing conditions, a representation formula is proved using the Fourier transform and tempered distributions. Ideas from integral geometry are used to apply the functional J\spα to irregularities of distribution, and estimates of discrepancy are obtained for measures that do not have atoms. Finally, the close relation between $J\sp1$ and the Radon transform is investigated. Inequalities are deduced that bound certain norms of the Radon transform away from zero.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Rogers, Allen Dale

Contributors dc:contributor

• Alexander, J. Ralph

• Mathematics

Statement dc:rights

• Copyright 1990 Rogers, Allen Dale

Language dc:language

eng

Identifier

AAI9114391
(UMI)AAI9114391

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/21952