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The problem of moments on polytopes and other bounded regions

✍ Scribed by Richard H. Stockbridge

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
177 KB
Volume
285
Category
Article
ISSN
0022-247X

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✦ Synopsis

The problem of moments is considered for polytopes in R d and other bounded regions specified piecewise by curves of the form c 1 x

Necessary and sufficient conditions are suggested by a simple geometric observation. For some choices of c 1 , . . . , c d and Ξ± 1 , . . . , Ξ± d , these conditions reduce to the conditions of Hausdorff for the unit interval, of Hildebrandt and Schoenberg for the unit square and of Dale for the unit simplex in R 2 , whereas for other choices new conditions are required. The proofs are obtained using probabilistic techniques.

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