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Some Moment Problems in a Finite Interval

Published online by Cambridge University Press:  20 November 2018

D. Leviatan*
Affiliation:
Tel-Aviv University, Tel-Aviv, Israel; University of Illinois, Urbana, Illinois
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Let the sequence {λi} (i ≧ 0) satisfy the following conditions.

1.

2.

3.

We shall deal with the following moment problems: what are the conditions, necessary and sufficient, on a sequence {μn} (n ≧ O) in order that it should possess the representation

1.1

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Hausdorff, F., Summationsmethoden und momentenfolgen. II, Mat. Z. 5 (1921), 280299.10.1007/BF01279032CrossRefGoogle Scholar
2. Krasnosel'skiï, M. A. and Rutickiï, Ya. B., Convex function and Orlicz spaces (P. Noordhoff, Grôningen, 1961).Google Scholar
3. Leviatan, D., A generalized moment problem, Israel J. Math. 5 (1967), 97103.Google Scholar
4. Lorentz, G. G., Bernstein polynomials (Univ. Toronto Press, Toronto, 1953).Google Scholar
5. Medvedev, Ju. I., Generalization of a theorem of F. Riesz, Uspehi Mat. Nauk 8 (1953), 115118.Google Scholar
6. Schoenberg, I. J., On finite rowed system ôf linear inequalities in infinitely many variables, Trans. Amer. Math. Soc. 34 (1932), 594619.Google Scholar
7. Widder, D. V., The Laplace transform (Princeton, 1946).Google Scholar
8. Zygmond, A., Trigonometric series. I, 2nd ed. (Cambridge Univ. Press, Cambridge, 1959).Google Scholar