ON A MOMENT PROBLEM

Abstract

Let n_0 be any fixed non-negative integer, - ∞ ≤ a<b ≤ ∞ and f(x) ≥ 0 an absolutely continuous function with f'(x) \ e 0, a.e. on (a, b). Then the sequence of functions { {(f(x))^n}{e ^{- f(x)}}} _{n = {n_0}}^∞ is complete in L(a, b) if and only if the function f(x) is strictly monotone on (a, b).