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Properties of Littlewood-Paley sets

Published online by Cambridge University Press:  04 October 2011

Kathryn E. Hare  and
Ivo Klemes
Kathryn E. Hare
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Ivo Klemes
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6, Canada
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Abstract

We give a combinatorial characterization of the known examples of intervals of ℤ having the Littlewood-Paley (LP) property. This leaves an interesting open problem. We also note that certain previously known necessary conditions are equivalent, and give two examples of intervals which are not LP but whose endpoints form thin sets (e.g. Sidon or Λ(p) for all p < ∞).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 485 - 494
Copyright
Copyright © Cambridge Philosophical Society 1989

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