Journal article
Moment problems in an infinite number of variables
Infinite dimensional analysis, quantum probability, and related topics, Vol.18(4), p.1550024
12/01/2015
DOI: 10.1142/S0219025715500241
Abstract
Let R-infinity = X-d = 1(infinity) R. Given a closed set K subset of R-infinity and s : S-* -> R, where S-* denotes the set of tuples of nonnegative integers ( n(1), n(2), ...) with n(d) > 0 for finitely many d, the K-moment problem on R-infinity entails determining whether or not there exists a measure sigma on R-infinity so that supp sigma subset of K and
s(n) = integral(R infinity) x(n) d sigma(x) for all n is an element of S-*.
We prove that sigma exists if and only if a natural analogue of the Riesz-Haviland functional L-s is K-positive, i. e. if p(x) = Sigma(0 <=vertical bar n vertical bar <= m) p(n) x(n) is any polynomial which is nonnegative for all x is an element of K, then
L-s (p) = Sigma(0 <=vertical bar n vertical bar <= m) p(n) s(n) >= 0.
We will also provide a sufficient condition for sigma to be unique, an analogue of a celebrated theorem of K. Schmoudgen and an application to stochastic processes.
Details
- Title: Subtitle
- Moment problems in an infinite number of variables
- Creators
- Daniel Alpay - Ben-Gurion University of the NegevPalle E. T Jorgensen - University of IowaDavid P Kimsey - Ben-Gurion University of the Negev
- Resource Type
- Journal article
- Publication Details
- Infinite dimensional analysis, quantum probability, and related topics, Vol.18(4), p.1550024
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- DOI
- 10.1142/S0219025715500241
- ISSN
- 0219-0257
- eISSN
- 1793-6306
- Number of pages
- 14
- Language
- English
- Date published
- 12/01/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984240861302771
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