Vol. 15, No. 1, 1965

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ISSN: 0030-8730
A note on Hausdorff's summation methods

Joseph Patrick Brannen

Vol. 15 (1965), No. 1, 29–33
Abstract

If {an} is a moment sequence and (Δa) is the difference matrix having base sequence {an}, then (Δa) is symmetric about the main diagonal if and only if the function α(x) such that an =01xndα(x),n = 0,1,2,, is symmetric in the sense that α(x) + α(1 + x) = α(1) + α(0) except for at most countably many x in [0,1]. This property is related to the “fixed points” of the matrix H, where HaH is the Hausdorff matrix determined by the moment sequence {an}.

Mathematical Subject Classification
Primary: 40.30
Milestones
Received: 15 March 1964
Published: 1 March 1965
Authors
Joseph Patrick Brannen