Sets of Divergence of Fourier Series.
Singular distributions, dimension of support, and symmetry of Fourier transform
We study the “Fourier symmetry” of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are:(i) A one-side extension of Frostman’s theorem, which connects the rate of decay of Fourier transform of a distribution with the Hausdorff dimension of its support;(ii) A construction of compacts of “critical” size, which support distributions (even pseudo-functions) with anti-analytic part belonging to .We also give examples of non-symmetry...
Smooth rough paths and applications to Fourier analysis.
Some absolutely effective product methods.
Some new modified cosine sums and -convergence of cosine trigonometric series
In this paper we introduce some new modified cosine sums and then using these sums we study -convergence of trigonometric cosine series.
Some remarks on quasi-Cohen sets
We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.
Some remarks on strong approximation by Cesàro means
Some results on -approximation of the -th derivate of Fourier series.
Sommes partielles des séries de Fourier
Spaces of functions of generalized bounded variation. II: Questions of uniform convergence of Fourier series.
Sur la convergence uniforme des séries de Fourier.