Moment Problem
المؤلف:
Hausdorff, F.
المصدر:
"Summationsmethoden und Momentfolgen. I." Math. Z. 9
الجزء والصفحة:
...
22-2-2021
2261
Moment Problem
The moment problem, also called "Hausdorff's moment problem" or the "little moment problem," may be stated as follows. Given a sequence of numbers ![<span style=]()
{mu_n}_(n=0)^infty" src="https://mathworld.wolfram.com/images/equations/MomentProblem/Inline1.gif" style="height:17px; width:43px" />, under what conditions is it possible to determine a function 
of bounded variation in the interval 
such that
for 
, 1, .... Such a sequence is called a moment sequence, and Hausdorff (1921ab) was the first to obtain necessary and sufficient conditions for a sequence to be a moment sequence.
REFERENCES:
Hausdorff, F. "Summationsmethoden und Momentfolgen. I." Math. Z. 9, 74-109, 1921a.
Hausdorff, F. "Summationsmethoden und Momentfolgen. II." Math. Z. 9, 280-299, 1921b.
Leviatan, D. "A Generalized Moment Problem." Israel J. Math. 5, 97-103, 1967.
Widder, D. V. "The Moment Problem." Ch. 3 in The Laplace Transform. Princeton, NJ: Princeton University Press, pp. 100-101, 1941.
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