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Weakly almost periodic functions and thin sets in discrete groups

Ching Chou
1990 Transactions of the American Mathematical Society  
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 I P -norm  ...  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.  ...  For abelian G, a weak p-Sidon set is just a p-Sidon set as defined by Edwards and Ross [7] . Note also that (weak) I-Sidon sets are just (weak) Sidon sets as defined by Picardello [15] .  ... 
doi:10.1090/s0002-9947-1990-0984855-6 fatcat:6sjstpvjwvheve2wbl7s572yzi

Weakly Almost Periodic Functions and Thin Sets in Discrete Groups

Ching Chou
1990 Transactions of the American Mathematical Society  
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 I P -norm  ...  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.  ...  For abelian G, a weak p-Sidon set is just a p-Sidon set as defined by Edwards and Ross [7] . Note also that (weak) I-Sidon sets are just (weak) Sidon sets as defined by Picardello [15] .  ... 
doi:10.2307/2001605 fatcat:llsfqva7cjfudnlffpfxhdzmru

On Fourier-Stieltjes transforms of continuous measures

Ron C Blei
1977 Journal of Functional Analysis  
The continuous measure whose transform equals 1 on a non-Sidon portion of (JL, Ej C E will be obtained as a weak* limit of trigonometric polynomials that are inductively defined below.  ...  Fix a sequence of positive prime integers, (pj), tending monotonically to infinity, and let EC E be a non-Sidon set.  ...  The continuous measure whose transform equals 1 on a non-Sidon portion of (JL, Ej C E will be obtained as a weak* limit of trigonometric polynomials that are inductively defined below.  ... 
doi:10.1016/0022-1236(77)90023-4 fatcat:wg6orvzxinbqzpmncdps4rtp54

Page 1784 of Mathematical Reviews Vol. 55, Issue 6 [page]

1978 Mathematical Reviews  
Then the quantity o(£)= sup{inf{||z||: A= on E}: pe 1 °(E), |\—|| . <1} is finite. A lacunary sequence in the integer group is an example of a Sidon set.  ...  Lecture Notes in Pure and Appl. Math., Vol. 2, Dekker, New York, 1971. Kronecker, Helson, Dirichlet, weak Kronecker, and weak Dirichlet sets are considered.  ... 

Largest cliques in connected supermagic graphs

Anna Lladó
2005 Discrete Mathematics & Theoretical Computer Science  
Bounds on Sidon sets show that the order of such a graph is at least $n^2+o(n^2)$.  ...  Moreover it can be required that the graph admits a supermagic labelling $f$, which satisfies the additional condition $f(V)=[1,|V|]$.  ...  On the other hand, the known constructions of dense Sidon sets together with results on the distribution of primes provide in particular weak Sidon sets of cardinality n in [1, N ] with N = n 2 + o(n  ... 
doi:10.46298/dmtcs.3414 fatcat:z45d6kkqobakpps5uokiuslxam

Arens regularity and weak sequential completeness for quotients of the Fourier algebra

Colin C. Graham
2000 Illinois Journal of Mathematics  
This is a study of Arens regularity in the context of quotients of the Fourier algebra on a non-discrete locally compact abelian group (or compact group). (1) If a compact set E of G is of bounded synthesis  ...  and is the support of a pseudofunction, then A (E) is weakly sequentially complete. ( This implies that every point of E is a Day point.) (2) If a compact set E supports a synthesizable pseudofunction  ...  (ii) Any weak* (tr(A(G)*, A(G)**)) accumulation point of a 1-tenting sequence on A(G) is an invariant mean on A(G)* [12] , [18]. See also Remark 2.5.1.  ... 
doi:10.1215/ijm/1255984689 fatcat:jlxpdd5a3jhf5o4vajvp3ltpl4

The Ubiquity of Sidon Sets That Are Not I_0 [article]

Kathryn E. Hare, L. Thomas Ramsey
2016 arXiv   pre-print
We prove that every infinite, discrete abelian group admits a pair of I_0 sets whose union is not I_0. In particular, this implies that every such group contains a Sidon set that is not I_0.  ...  We claim that {Π(λ n + χ n )} is weak ε q -Kronecker. To prove this, note that a character g on Λ is specified as g = {g n }, with each g n a character on Ω β n .  ...  Introduction A subset E of a discrete abelian group Γ with compact dual group G is said to be a Sidon set if every bounded E-sequence can be interpolated by the Fourier transform of a measure on G.  ... 
arXiv:1602.04241v1 fatcat:khzmr6hc5zhfjg252maubz57dy

Weakly almost periodic functions and Fourier-Stieltjes algebras of locally compact groups

Ching Chou
1982 Transactions of the American Mathematical Society  
But we do not have a proof yet.  ...  Therefore, the above proposition states that if 5 contains large squares then it is not a weak Sidon set. When G is abelian, a weak Sidon set is just a Sidon set in the usual sense.  ...  Using standard results in functional analysis, one sees that a set S in G is weak Sidon if and only if II • II, and II • ||" are equivalent on lx(S).  ... 
doi:10.1090/s0002-9947-1982-0670924-2 fatcat:n6hafhgi75fs5k7q2vxs3oiwv4

Largest cliques in connected supermagic graphs

A. Lladó
2007 European journal of combinatorics (Print)  
Bounds on Sidon sets show that the order of such a graph is at least n 2 +o(n 2 ).  ...  A graph G = (V, E) is said to be magic if there exists an integer labeling f : Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most 3n 2 + o(n 2 ) which contain a complete  ...  Let A = {a 1 < a 2 < • • • < a n } ⊂ [1, N ] be a weak Sidon set. Since Aa 1 + 1 is a weak Sidon set as well, we may assume that a 1 = 1.  ... 
doi:10.1016/j.ejc.2007.04.006 fatcat:efpa6zb6zzbgnijap22k6xlufi

Completely Sidon sets in C^*-algebras (New title) [article]

Gilles Pisier
2018 arXiv   pre-print
A sequence in a C^*-algebra A is called completely Sidon if its span in A is completely isomorphic to the operator space version of the space ℓ_1 (i.e. ℓ_1 equipped with its maximal operator space structure  ...  Our main result is a generalization to this context of Drury's classical theorem stating that Sidon sets are stable under finite unions.  ...  The predual M 1 * is the subset of M 1 * formed of the weak* continuous functionals on M 1 .  ... 
arXiv:1705.08680v4 fatcat:xu7634hrgzfllecpauud6kas7y

On uniformly bounded orthonormal Sidon systems [article]

Gilles Pisier
2016 arXiv   pre-print
This sharpens their result that it is 5-fold tensor Sidon. The proof is somewhat reminiscent of the author's original one for (Abelian) group characters, based on ideas due to Drury and Rider.  ...  In the latter setting we also include a new proof of Rider's unpublished result that randomly Sidon sets are Sidon, which implies that the union of two Sidon sets is Sidon.  ...  Let (ψ 1 n ) be a Sidon sequence. Then for any sequence (ψ 2 n ) such that δ = inf ψ 2 n 1 > 0, the sequence (ψ 1 n ⊗ ψ 2 n ) is Sidon.  ... 
arXiv:1602.02430v6 fatcat:5c2p552hgrc5hdazuc7m5cuivq

On uniformly bounded orthonormal Sidon systems

Gilles Pisier
2017 Mathematical Research Letters  
We also show that a uniformly bounded orthonormal system is randomly Sidon i it is ⊗ 4 tensor Sidon, or equivalently ⊗ k -Sidon for some (or all) k ≥ 4.  ...  In the latter setting we also include a new proof of Rider's unpublished result that randomly Sidon sets are Sidon, which implies that the union of two Sidon sets is Sidon.  ...  A sequence (ϕ n ) of distinct irreducible representations on a compact group is Sidon iff it is randomly Sidon. Corollary 5. e ij ⊗ e ij .  ... 
doi:10.4310/mrl.2017.v24.n3.a13 fatcat:r45f2j5quzbz7f6k6ae4xon5bu

Sidon Sequences and Doubly Periodic Two-Dimensional Synchronization Patterns [article]

Tuvi Etzion
2011 arXiv   pre-print
A few constructions of two-dimensional synchronization patterns are based on these sequences.  ...  We also present a new construction for Sidon sequences over an alphabet of size q(q-1), where q is a power of a prime.  ...  D is a Sidon sequence (or a B 2 -sequence) over A if all the sums a i1 + a i2 with 1 ≤ i 1 ≤ i 2 ≤ m are distinct (if i 1 < i 2 in the definition the sequence is called a weak Sidon sequences).  ... 
arXiv:1102.2986v1 fatcat:jy4mdt4qknerdgvs7vab6fdva4

An upper bound on the size of Sidon sets [article]

József Balogh, Zoltán Füredi, Souktik Roy
2021 arXiv   pre-print
We show that the maximum size of a Sidon set of { 1, 2, ..., n} is at most √(n)+ 0.998n^1/4 for sufficiently large n.  ...  In this entry point into the subject, combining two elementary proofs, we decrease the gap between the upper and lower bounds by 0.2% in a classical combinatorial number theory problem.  ...  Note that for Sidon sets we need this to hold for i ≤ j. Denote by W (n) the size of the largest weak Sidon subset of [n].  ... 
arXiv:2103.15850v2 fatcat:pnfncdgwejarldzcrspmz7uuv4

Fourier-Stieltjes Transforms which vanish at infinity off certain sets

Louis Pigno
1978 Glasgow Mathematical Journal  
The method of Theorem 2 shows that the union of a weak Rajchman set and a Sidon set is a weak Rajchman set.  ...  A proof for arbitrary discrete T that a Sidon set is a Rajchman set can be based on Theorem 1.4 of [16, p. 8] and the method of proof of the present example. strong Riesz set.  ...  Note added in proof. The author has recently learned of the work of Keiji Izuchi, Sidon sets and small M 0 -sets, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 12 (1974), 146-148.  ... 
doi:10.1017/s0017089500003360 fatcat:gwthzt6htfextdnunouwp7oq4u
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