Walsh series with coefficients tending monotonically to zero

John Edward Coury

Vol. 54 (1974), No. 2, 1–16

DOI: 10.2140/pjm.1974.54.1

Abstract

Results conceming the Walsh-Fourier coefficients of continuous functions are obtained which extend the work of Bockarev to the case of nonabsolutely convergent Walsh series. Analogues of results for trigonometric series with monotonically decreasing coefficients are proven for the Walsh system. In particular, it is shown that, unlike the trigonometric case, convexity of the coefficlents is not sufficient to guarantee that such series are always nonnegative.

Mathematical Subject Classification

Primary: 42A56

Milestones

Received: 8 June 1973

Published: 1 October 1974