Moment sequences in Hilbert space

Gordon G. Johnson

Vol. 46 (1973), No. 1, 201–207

DOI: 10.2140/pjm.1973.46.201

Abstract

Suppose f is a real valued function of bounded variation on [0,1]. Then for each nonnegative integer n, the Stieltjes integral ∫ ₀¹jⁿdf exists, where for each number x,j(x) = x. A necessary and sufficient condition is given for f in order that the moment sequence for f,{C_n}_n=0^∞, is square summable. A second result establishes that the set of all such square summable moment sequences is dense in l².

Mathematical Subject Classification

Primary: 44A50

Milestones

Received: 7 January 1972

Revised: 24 April 1972

Published: 1 May 1973