Vol. 24, No. 1, 1968

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Some properties of sequences, with an application to noncontinuable power series

Francis William Carroll

Vol. 24 (1968), No. 1, 45–50
Abstract

For a real sequence f = {f(n)} and positive integer N, let FN denote the sequence of N-tuples {(f(n + 1),,f(n + N))}. A functional equation method due to Kemperman is used to obtain a sufficient condition on s in order that sN have an independent N-tuple among its cluster points. If a bounded s has the latter property, and if g = rs, where r(n) →∞ and r(n + 1)∕r(n) 1 as n →∞, then there is a subsequence S of the sequence of positive integers such that, for almost all real α, the restriction of αgN to S is uniformly distributed ( mod 1) in the N-cube.

Mathematical Subject Classification
Primary: 10.33
Milestones
Received: 19 September 1966
Published: 1 January 1968
Authors
Francis William Carroll