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|
Positive sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Positive_sequence&oldid=12427