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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A functional from geometry with applications to discrepancy estimates and the Radon transform


Author: Allen D. Rogers
Journal: Trans. Amer. Math. Soc. 341 (1994), 275-313
MSC: Primary 11K38; Secondary 44A12
DOI: https://doi.org/10.1090/S0002-9947-1994-1169082-8
MathSciNet review: 1169082
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Abstract: Estimates of discrepancy, or irregularities of distribution, are obtained for measures without atoms. Two estimators are used, the half-space, or separation, discrepancy $ {D_S}$ and a geometric functional $ {I^\alpha }$. A representation formula for the generalized energy integral $ {I^\alpha }$ is developed. Norm inequalities for the Radon transform are obtained as an application of the continuous discrepancy results. Integral geometric notions play a prominent role.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1169082-8
Keywords: Discrepancy, irregularities of distribution, generalized energy integral, metric geometry, integral geometry, Radon transform
Article copyright: © Copyright 1994 American Mathematical Society