arXiv subjects
Publications and source records attributed to Isabelle Chalendar.
For truncated Toeplitz operators, which are compressions of multiplication operators to model subspaces of the Hardy space $H^2$, we obtain criteria for commutation relations. The results show an analogy to the case of Toeplitz matrices, and they extend the theory of Sedlock algebras.
This paper determines the group of continuous invariants corresponding to an inner function $ Θ$ with finitely many singularities on the unit circle $T$; that is, the continuous mappings $g: T \to T$ such that $Θ\circ g = Θ$ on $\T$. These mappings form a group under composition.
We discuss boundedness and compactness properties of the embedding $M_Λ^1\subset L^1(μ)$, where $M_Λ^1$ is the closure of the monomials $x^{λ_n}$ in $L1([0,1])$ and $μ$ is a finite positive Borel measure on the interval $[0,1]$. In particular, we introduce a class of "sublinear" measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $Λ$. Finally, we show how one can recapture some of Al Alam's results on boundedness and essential norm of weighted composition operators from $M_Λ^1$ to $L1([0,1])$.
Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies the existence of a bounded symbol; the second is the reproducing kernel thesis. We show that in general the answer to the first question is negative, and we exhibit some classes of spaces for which the answers to both questions are positive.
An elementary lemma is used in order to show that the natural inclusion $J_p\to J_q$ of James spaces is superstrictly singular for $p<q$. As a consequence, it is shown that an operator without nontrivial invariant subspaces constructed by Charles Read is superstrictly singular.
We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragmén--Lindelöf-type theorem for analytic functions on ${\mathbb{C}}_+^n$.