Structure and existence of sidon sets on compact groups

Sidon Sets in Groups and Induced Subgraphs of Cayley Graphs

Let S be a subset of a group G. We call S a Sidon subset of the first (second) kind, if for any x, y, Z, WE S of which at least 3 are different, xy ~ ZW (xy I "" zwI , resp.). (For abelian groups, the two notions coincide.) If a has a Sidon subset of the second kind with n elements then every n-vertex graph is an induced subgraph of some Cayley graph of G. We prove that a sufficient condition f...

On Multiplicative Sidon Sets

Fix integers b > a ≥ 1 with g := gcd(a, b). A set S ⊆ N is {a, b}-multiplicative if ax 6= by for all x, y ∈ S. For all n, we determine an {a, b}-multiplicative set with maximum cardinality in [n], and conclude that the maximum density of an {a, b}-multiplicative set is b b+g . Erdős [2, 3, 4] defined a set S ⊆ N to be multiplicative Sidon1 if ab = cd implies {a, b} = {c, d} for all a, b, c, d ∈...

On Uniformly Approximable Sidon Sets

Let G be a compact abelian group and let T be the character group of G. Suppose £ is a subset of T. A trigonometric polynomial f on G is said to be an ^-polynomial if its Fourier transform / vanishes off E. The set E is said to be a Sidon set if there is a positive number B such that 2^xeb |/(X)| á-B||/||u for all E-polynomials /; here, ||/||„ = sup{ |/(x)| : xEG}. In this note we shall discuss...

Pseudoframe multiresolution structure on abelian locally compact groups

‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

Sumsets of Sidon sets