Weakly almost periodic functions and thin sets in discrete groups

Author:

Chou Ching

Abstract

A subset E E of an infinite discrete group G G is called (i) an R W {R_W} -set if any bounded function on G G supported by E E is weakly almost periodic, (ii) a weak p p -Sidon set ( 1 p > 2 ) (1 \leq p > 2) if on l 1 ( E ) {l^1}(E) the l p {l^p} -norm is bounded by a constant times the maximal C {C^*} -norm of l 1 ( G ) {l^1}(G) , (iii) a T T -set if x E E xE \cap E and E x E Ex \cap E are finite whenever x e x \ne e , and (iv) an F T FT -set if it is a finite union of T 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 G contains an R W {R_W} -set which is not an F T FT -set; (b) countable weak p p -Sidon sets, 1 p > 4 / 3 1 \leq p > 4/3 are F T FT -sets.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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