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.

Hamburger moment problem

For the Hamburger moment problem, 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 is determinate; that is, μ is the only measure on R with as its sequence of moments.

Stieltjes moment problem

For the Stieltjes moment problem, the sufficient condition for determinacy is