Carleman's condition
In mathematics, particularly, in analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. That is, if a measure μ satisfies Carleman's condition, there is no other measure ν having the same moments as μ. The condition was discovered by Torsten Carleman in 1922.[1]
Hamburger moment problem
For the Hamburger moment problem (the moment problem on the whole real line), the theorem states the following:
Let μ be a measure on R such that all the moments
are finite. If
then the moment problem for (mn) is determinate; that is, μ is the only measure on R with (mn) as its sequence of moments.
Stieltjes moment problem
For the Stieltjes moment problem, the sufficient condition for determinacy is
Notes
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References
- Akhiezer, N. I. (1965). The Classical Moment Problem and Some Related Questions in Analysis. Oliver & Boyd.CS1 maint: ref=harv (link)
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