Functions represented by Rademacher series

James R. McLaughlin

Vol. 27 (1968), No. 2, 373–378

DOI: 10.2140/pjm.1968.27.373

Abstract

A series of the form ∑ _m=1^∞a_mr_m(t), where {a_m} is a sequence of real numbers and r_m(t) denotes the m-th Rademacher function, sign sin(2^mπt), 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 {a_m} 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