Yanick Heurteaux
Multifractal analysis of the divergence of Fourier series.
Чт, 03/17/2011 - 16:01 — SomNambulAuthors: Yanick Heurteaux, Frédéric Bayart
Subjects: Classical Analysis and ODEs
AbstractA famous theorem of Carleson says that, given any function $f\in L^p(\TT)$,
$p\in(1,+\infty)$, its Fourier series $(S_nf(x))$ converges for almost every
$x\in \mathbb T$. Beside this property, the series may diverge at some point,
without exceeding $O(n^{1/p})$. We define the divergence index at $x$ as the
infimum of the positive real numbers $\beta$ such that $S_nf(x)=O(n^\beta)$ and
we are interested in the size of the exceptional sets $E_\beta$, namely the
sets of $x\in\mathbb T$ with divergence index equal to $\beta$.- Читать далее
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Measures and the Law of the Iterated Logarithm.
Пнд, 04/12/2010 - 15:01 — SomNambulAuthors: Imen Bhouri, Yanick Heurteaux
Subjects: Probability
AbstractLet m be a unidimensional measure with dimension d. A natural question is to
ask if the measure m is comparable with the Hausdorff measure (or the packing
measure) in dimension d. We give an answer (which is in general negative) to
this question in several situations (self-similar measures, quasi-Bernoulli
measures). More precisely we obtain fine comparisons between the mesure m and
generalized Hausdorff type (or packing type) measures. The Law of the Iterated
Logarithm or estimations of the L^q-spectrum in a neighborhood of q=1 are the
tools to obtain such results.
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