Central Lacunary Sets.
Certain lacunary cosine series are recurrent
Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.
Characterizing Sidon sets by interpolation properties of subsets
Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups containing...
Charakterisierungen von nirgends differenzierbaren Weierstraß-Funktionen durch Replikativität.
Complex Unconditional Metric Approximation Property for spaces
We study the Complex Unconditional Metric Approximation Property for translation invariant spaces of continuous functions on the circle group. We show that although some “tiny” (Sidon) sets do not have this property, there are “big” sets Λ for which has (ℂ-UMAP); though these sets are such that contains functions which are not continuous, we show that there is a linear invariant lifting from these spaces into the Baire class 1 functions.
Comportement local des fonctions à série de Fourier lacunaire