Comparison of Haar series with gaps with trigonometric series

James R. McLaughlin and Justin Jesse Price

Vol. 28 (1969), No. 3, 623–627

DOI: 10.2140/pjm.1969.28.623

Abstract

We study Haar series with gaps and show striking differences between these series and lacunary trigonometric series. For example, we prove that under certain gap conditions Haar series are finite series almost everywhere.

Mathematical Subject Classification

Primary: 42.16

Milestones

Received: 26 April 1968

Published: 1 March 1969