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Carleman's condition
Encyclopedia
In mathematics, Carleman's condition is a sufficient condition for the determinacy of the moment problem.
, states the following:
Let μ be a measure
on R such that all the moments
![](http://image.absoluteastronomy.com/images/formulas/3/4/3347428-1.gif)
are finite. If![](http://image.absoluteastronomy.com/images/formulas/3/4/3347428-2.gif)
then the moment problem for mn is determinate; that is, μ is the only measure on R with (mn) as its sequence of moments.
Hamburger moment problem
For the Hamburger moment problem, the theorem, proved by Torsten CarlemanTorsten Carleman
Torsten Carleman , born Tage Gills Torsten Carleman, was a Swedish mathematician....
, states the following:
Let μ be a measure
Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...
on R such that all the moments
![](http://image.absoluteastronomy.com/images/formulas/3/4/3347428-1.gif)
are finite. If
![](http://image.absoluteastronomy.com/images/formulas/3/4/3347428-2.gif)
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![](http://image.absoluteastronomy.com/images/formulas/3/4/3347428-3.gif)