منابع مشابه
Some Thin Sets in Discrete Abelian Groups 57
Let T be a discrete abelian group, and E C T. For F C E, we say that F e 9(E), if for all A, finite subsets of I", 0 / A, A + F n F is finite. Having defined the Banach algebra, A(E) = c(E) n B(E), we prove the following: (i) E C T is a Sidon set if and only if every F e 9(E) is a Sidon set; (ii) E e?(r) is a Sidon set if and only if A(E) = A(E). 0. Introduction. Let L denote a discrete abelian...
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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 s...
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If G is an abelian group of order u, and D is a subset of G with k elements such that every nonidentity element can be expressed 2 times in the form a b, where a and b are elements of D, then D is called a (u, k, A) difference set in G. The order n of the difference set is k 1. In this paper we consider the parameter values v = 22di 2, k = 22d+ ’ 24 ,I= 22d 2d, and n=22d. The rank r of G is the...
متن کاملSum-free Sets in Abelian Groups
Let A be a subset of an abelian group G with |G| = n. We say that A is sum-free if there do not exist x, y, z ∈ A with x+ y = z. We determine, for any G, the maximal density μ(G) of a sum-free subset of G. This was previously known only for certain G. We prove that the number of sum-free subsets of G is 2, which is tight up to the o-term. For certain groups, those with a small prime factor of t...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.2307/1996900