arXiv subjects
Publications and source records attributed to Reda Choukrallah.
Le but de cet article est d'obtenir la cyclicite de certaines classes de fonctions pour des operateurs de Toeplitz anti-analytique associes a un produit fini de Blaschke dans les espaces $H^p$ ou $1<p<\infty$. Il s'agit aussi de decrire les sous-espaces invariants par ce type d'operateur et engendres par des decompositions lacunaires de fonctions.
This article gives a description of invariant subspaces for the backward shift generated by vector valued lacunary series and by a class of lacunary power series in $H^2(\mathbb{D}, X)$, (where $X$ is an Hilbert space). In particular, we show that these series $f$ in $H^2(\mathbb{D}, X)$ are cyclic vectors if and only if the queue of Taylor coefficients $\{\hat{f}(k)$, $k>N\}$ generates the whole space $X$. Analogues of this result are obtained for some functions whose spectrum is a finite union of lacunary sequences and in the polydisc. In the scalar case $H^2$, we give a criterion on the Fourier spectrum of the function to have cyclicity for any power of the backward shift.
We prove in the vector-valued spaces $L^2(\mathbb{R}_+, X)$ (where $X$ is a finite dimensional Hilbert space) the cyclicity for the semi-group of left translations of some particular functions with support included in a lacunary system of intervals.