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 , 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.