Vol. 24, No. 1, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
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