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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Weakly almost periodic functions and thin sets in discrete groups
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by Ching Chou PDF
Trans. Amer. Math. Soc. 321 (1990), 333-346 Request permission

Abstract:

A subset $E$ of an infinite discrete group $G$ is called (i) an ${R_W}$-set if any bounded function on $G$ supported by $E$ is weakly almost periodic, (ii) a weak $p$-Sidon set $(1 \leq p < 2)$ if on ${l^1}(E)$ the ${l^p}$-norm is bounded by a constant times the maximal ${C^*}$-norm of ${l^1}(G)$, (iii) a $T$-set if $xE \cap E$ and $Ex \cap E$ are finite whenever $x \ne e$, and (iv) an $FT$-set if it is a finite union of $T$-sets. In this paper, we study relationships among these four classes of thin sets. We show, among other results, that (a) every infinite group $G$ contains an ${R_W}$-set which is not an $FT$-set; (b) countable weak $p$-Sidon sets, $1 \leq p < 4/3$ are $FT$-sets.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 333-346
  • MSC: Primary 43A46; Secondary 43A07, 43A30, 43A60
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0984855-6
  • MathSciNet review: 984855