A FUNCTIONAL FROM GEOMETRY WITH APPLICATIONS TO DISCREPANCY ESTIMATESAND THE RADON-TRANSFORM

Authors
ROGERS AD
Citation
Ad. Rogers, A FUNCTIONAL FROM GEOMETRY WITH APPLICATIONS TO DISCREPANCY ESTIMATESAND THE RADON-TRANSFORM, Transactions of the American Mathematical Society, 341(1), 1994, pp. 275-313
Citations number
31
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
341
Issue
1
Year of publication
1994
Pages
275 - 313
Database
ISI
SICI code
0002-9947(1994)341:1<275:AFFGWA>2.0.ZU;2-W
Abstract
Estimates of discrepancy, or irregularities of distribution, are obtai ned for measures without atoms. Two estimators are used, the half-spac e, or separation, discrepancy D-S and a geometric functional I-alpha. A representation formula for the generalized energy integral I-alpha i s developed. Norm inequalities for the Radon transform are obtained as an application of the continuous discrepancy results. Integral geomet ric notions play a prominent role.