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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lacunary sets based on Lorentz spaces
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by Raymond J. Grinnell PDF
Proc. Amer. Math. Soc. 127 (1999), 3547-3556 Request permission

Abstract:

A new lacunary set for compact abelian groups is introduced; this is called a $\Lambda (p,q)$ set. This set is defined in terms of the Lorentz spaces and is shown to be a generalization of $\Lambda (p)$ sets and Sidon sets. A number of functional-analytic statements about $\Lambda (p,q)$ sets are established by making use of the structural similarities between $L^{p}$ spaces and Lorentz spaces. These statements are analogous to several well-known properties of a set which are equivalent to the definition of a $\Lambda (p)$ set. Some general set-theoretic and arithmetic properties of $\Lambda (p,q)$ sets are also developed; these properties extend known results on the structure of $\Lambda (p)$ sets. Open problems and directions for further research are outlined.
References
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Additional Information
  • Raymond J. Grinnell
  • Affiliation: Department of Computer Science, Mathematics & Physics, University of the West Indies, Cave Hill Campus, P.O. Box 64, Bridgetown, Barbados, West Indies
  • Email: grinnell@uwichill.edu.bb
  • Received by editor(s): September 5, 1996
  • Received by editor(s) in revised form: February 12, 1998
  • Published electronically: May 13, 1999
  • Communicated by: J. Marshall Ash
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3547-3556
  • MSC (1991): Primary 43A46; Secondary 43A15, 43A25
  • DOI: https://doi.org/10.1090/S0002-9939-99-04918-7
  • MathSciNet review: 1610901