Positive sequence

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A sequence of real numbers in the interval such that for any polynomial

that is not identically zero and is not negative on the expression

If for any such polynomial , then the sequence is called strictly positive. For the sequence in to be positive, the existence of an increasing function on for which


is necessary and sufficient.


A (strictly) negative sequence can be similarly defined and has a similar property. The problem of deciding whether for a given sequence of real numbers there is a positive Borel measure on such that is known as the Hamburger moment problem. The condition (1) is a moment condition, cf. Moment problem.


[a1] H.J. Landau (ed.) , Moments in mathematics , Amer. Math. Soc. (1987) pp. 56ff
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Positive sequence. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article