Weakly Almost Periodic Functions and Thin Sets in Discrete Groups
نویسنده
چکیده
A subset E of an infinite discrete group G is called (i) an Rw-set if any bounded function on G supported by E is weakly almost periodic, (ii) a weak p-Sidon set (1 ~ p < 2) if on II (E) the IP -norm is bounded by a constant times the maximal C·-norm of I\G) , (iii) a T-set if xE n E and Ex n E are finite whenever x of 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 Rw-set which is not an FT-set; (b) countable weak p-Sidon sets, 1 ~ P < 4/3 are F T -sets.
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