Vol. 27, No. 2, 1968

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Functions represented by Rademacher series

James R. McLaughlin

Vol. 27 (1968), No. 2, 373–378
Abstract

A series of the form m=1amrm(t), where {am} is a sequence of real numbers and rm(t) denotes the m-th Rademacher function, sign sin(2mπt), is called a Rademacher series (as usual, sign 0 = 0).

Letting f(t) denote the sum of this series whenever it exists, we shall investigate the effect that various conditions on {am} have on the continuity, variation, and differentiability properties of f.

Mathematical Subject Classification
Primary: 42.16
Milestones
Received: 27 June 1967
Published: 1 November 1968
Authors
James R. McLaughlin