Vol. 45, No. 2, 1973

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Some results on lacunary Walsh series

John Edward Coury

Vol. 45 (1973), No. 2, 419–425
Abstract

It is known that if a lacunary trigonometric series converges to 0 on a set of positive measure, then the series vanishes identically. In the present paper, the following analogue for the Walsh system is proved: a lacunary Walsh series which converges to 0 almost everywhere is identically zero.

Mathematical Subject Classification
Primary: 42A44
Milestones
Received: 3 December 1971
Revised: 16 June 1972
Published: 1 April 1973
Authors
John Edward Coury