Helson sets and simultaneous extensions to Fourier transforms
How to recognize a true Σ^0_3 set
Let X be a Polish space, and let be a sequence of hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether is a true subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true .
Images of Gaussian random fields: Salem sets and interior points
Let be a Gaussian random field in with stationary increments. For any Borel set , we provide sufficient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt [24] and Kahane [12,13] for fractional Brownian motion.
Interpolation by the Fourier-Stieltjes transform of a positive compactly supported measure
Interpolation harmonique sur les compacts
Interpolation sets for Fréchet measures
We introduce various classes of interpolation sets for Fréchet measures-the measure-theoretic analogues of bounded multilinear forms on products of C(K) spaces.
Lacunarity on Compact Hypergroups.
Lacunary series on compact groups
A theorem of Sidon concerning absolutely convergent Fourier series is extended to compact groups.
L'espace des fonctions presque-périodiques dont le spectre est contenu dans un ensemble compact dénombrable a la propriété de Schur
Means on -subspaces of with RNP and Schur property
Let be a locally compact abelian group and be the space of bounded convolution...
Measures and lacunary sets
We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
Metric unconditionality and Fourier analysis
We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between and . These...
On Bohr cluster sets
On concentrated sets and N-sets
On Ditkin sets
In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter’s terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3]) are mentioned...
On harmonic separation
On Hilbert sets and -spaces with no subspace isomorphic to
On inclusions between Arbault sets
On partitioning Sidon sets with quasi-independent sets
On Primary Ideals in the Group Algebra of a Nilpotent Lie Group.