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The truncated moment problem on N0

Infusino, M., Kuna, T., Lebowitz, J. L. and Speer, E. R. (2017) The truncated moment problem on N0. Journal of Mathematical Analysis and Applications, 452 (1). pp. 443-468. ISSN 0022-247X

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To link to this item DOI: 10.1016/j.jmaa.2017.02.060

Abstract/Summary

We find necessary and sufficient conditions for the existence of a probability measure on N0, the nonnegative integers, whose first n mo- ments are a given n-tuple of nonnegative real numbers. The results, based on finding an optimal polynomial of degree n which is nonneg- ative on N0 (and which depends on the moments), and requiring that its expectation be nonnegative, generalize previous results known for n = 1, n = 2 (the Percus-Yamada condition), and partially for n = 3. The conditions for realizability are given explicitly for n ≤ 5 and in a finitely computable form for n ≥ 6. We also find, for all n, explicit bounds, in terms of the moments, whose satisfaction is enough to guarantee realizability. Analogous results are given for the truncated moment problem on an infinite discrete semi-bounded subset of R.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:66418
Publisher:Elsevier

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