In mathematics, particularly, in analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. That is, if a measure satisfies Carleman's condition, there is no other measure having the same moments as The condition was discovered by Torsten Carleman in 1922.[1]
Hamburger moment problem
editFor the Hamburger moment problem (the moment problem on the whole real line), the theorem states the following:
Let be a measure on such that all the moments
Stieltjes moment problem
editFor the Stieltjes moment problem, the sufficient condition for determinacy is
Notes
editReferences
edit- Akhiezer, N. I. (1965). The Classical Moment Problem and Some Related Questions in Analysis. Oliver & Boyd.
- Chapter 3.3, Durrett, Richard. Probability: Theory and Examples. 5th ed. Cambridge Series in Statistical and Probabilistic Mathematics 49. Cambridge ; New York, NY: Cambridge University Press, 2019.