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Hervé Queffélec

Publications and source records attributed to Hervé Queffélec.

48 records · Page 3Linked to original sources
arXiv2010

Compact composition operators on Bergman-Orlicz spaces

We construct an analytic self-map $ϕ$ of the unit disk and an Orlicz function $Ψ$ for which the composition operator of symbol $ϕ$ is compact on the Hardy-Orlicz space $H^Ψ$, but not compact on the Bergman-Orlicz space ${\mathfrak B}^Ψ$. For that, we first prove a Carleson embedding theorem, and then characterize the compactness of composition operators on Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2.

math.FA↗
arXiv2010

Some revisited results about composition operators on Hardy spaces

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^Ψ$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^Ψ$; construction of a surjective symbol whose composition operator is compact on $H^Ψ$ and, moreover, is in all the Schatten classes $S_p (H^2)$, $p > 0$. On the other hand, we revisit the classical case of composition operators on $H^2$, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu.

math.FA↗
arXiv2009

Some new thin sets of integers in Harmonic Analysis

We randomly construct various subsets $Λ$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in $Λ$ have uniformly convergent series, and their Fourier coefficients are in $\ell_p$ for all $p>1$; moreover, all the Lebesgue spaces $L^q_Λ$ are equal for $q<+\infty$. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded functions with spectrum in $Λ$ is non separable. So these sets are very different from the thin sets of integers previously known.

math.FA↗
arXiv2009

On some random thin sets of integers

We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in {\sl Some new thin sets of integers in Harmonic Analysis, Journal d'Analyse Mathématique 86 (2002), 105--138}, namely that there exist 4/3-Rider sets which are sets of uniform convergence and $Λ(q)$-sets for all $q < \infty $, but which are not Rosenthal sets. In a second part, we show, using an older result of Kashin and Tzafriri that, for $p > {4/3}$, the $p$-Rider sets which we had constructed in that paper are almost surely ot of uniform convergence.

math.FA↗
arXiv2009

Composition operators on the Wiener-Dirichlet algebra

We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection between the properties of the operator and of its symbol, with special emphasis on the compact, automorphic, or isometric character of this operator. We are led to the intermediate study of algebras of functions of several, or countably many, complex variables.

math.FA↗
arXiv2009

Thin sets of integers in Harmonic analysis and p-stable random Fourier series

We investigate the behavior of some thin sets of integers defined through random trigonometric polynomial when one replaces Gaussian or Rademacher variables by p-stable ones, with 1 < p < 2. We show that in one case this behavior is essentially the same as in the Gaussian case, whereas in another case, this behavior is entirely different.

math.FA↗
arXiv2006

Composition operators on Hardy-Orlicz spaces

We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $Ψ$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded,..., and show how these notions behave according to the growth of $Ψ$. We introduce an adapted version of Carleson measure. We construct various examples showing that our results are essentially sharp. In the last part, we study the case of Bergman-Orlicz spaces.

math.FA↗
arXiv2004

Composition operators on the Wiener-Dirichlet algebra

In this paper, we study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. We study the connection between the properties of the operator and of its symbol, with special emphasis on the compact, automorphic, or isometric character of this operator. We are led to the intermediate study of algebras of functions of several, or countably many, complex variables.

math.FA↗