Vol. 34, No. 1, 1970

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On uniform convergence for Walsh-Fourier series

Cornelius W. Onneweer

Vol. 34 (1970), No. 1, 117–122

In 1940 R. Salem formulated a sufficient condition for a continuous and periodic function to have a trigonometric Fourier series which converges uniformly to the function. In this paper we will formulate a similar condition, which implies that the Walsh-Fourier series of such a function has this property. Furthermore we show that our result is stronger than certain classical results, and that it also implies the uniform convergence of the Walsh-Fourier series of certain classes of continuous functions of generalized bounded variation. The latter is analogous to results obtained by L. C. Young and R. Salem for trigonometric Fourier series.

Mathematical Subject Classification
Primary: 42.16
Received: 9 June 1969
Published: 1 July 1970
Cornelius W. Onneweer