Vol. 46, No. 1, 1973

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ISSN: 0030-8730
Moment sequences in Hilbert space

Gordon G. Johnson

Vol. 46 (1973), No. 1, 201–207
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,{Cn}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
Authors
Gordon G. Johnson