ABSTRACT
For each pair (a, b) such that –∞ ≤ a < b ≤ ∞ let Ψ(a, b) denote the family of distribution functions ψ(t) (i.e., real-valued, bounded, non-decreasing functions with infinitely many points of increase) on a < t < b. The Stieltjes moment problem (SMP) for a sequence { c n } n = 0 ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq268.tif"/> is to find necessary and sufficient conditions for there to exist a ψ ∈ Ψ(0, ∞) such that () c n = ∫ 0 ∞ ( − t ) n d ψ ( t ) , n = 0 , 1 , 2 , … . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq269.tif"/>
