101 citations · 131 across the 26 of their papers we have counts for
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Schäffer's matrix inequality: the exact asymptotic constant
Samy Houache, Oleg Szehr, Rachid Zarouf
Let denote the smallest constant such that \[ |\det T|\|T^{-1}\| \leq S_n \|T\|^{n-1} \] for every invertible operator on every -dimensional complex Banach space. In H…
Interpolation without commutants
Oleg Szehr, Rachid Zarouf
We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carathéodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed a…
Boundedness of the differentiation operator in model spaces and application to Peller type inequalities
Anton Baranov, Rachid Zarouf
Given an inner function in the unit disc , we study the boundedness of the differentiation operator which acts from from the model subspace $K\_Θ=\left(ΘH^{2}\right…
A model space approach to some classical inequalities for rational functions
Anton Baranov, Rachid Zarouf
We consider the set \mathcal{R}_{n} of rational functions of degree at most n\geq1 with no poles on the unit circle \mathbb{T} and its subclass \mathcal{R}_{n,\, r} consisting of r…
Iterated resolvent estimates for power bounded matrices
Rachid Zarouf
We discuss analogs of the Kreiss resolvent condition for power bounded matrices. We also explain how to extend it to analogs of the Hille-Yosida condition.
Application of a Bernstein type inequality to rational interpolation in the Dirichlet space
Rachid Zarouf
We prove a Bernstein-type inequality involving the Bergman and the Hardy norms, for rational functions in the unit disc \mathbb{D} having at most n poles all outside of \frac{1}{r}…