K. Fouchet

activity

20212025

collaborators

3 papers

math.FA2025

Sharp estimate on the resolvent of a finite-dimensional contraction

Karine Fouchet

We compute an asymptotic formula for the supremum of the resolvent norm ( $ζ$ -T ) -1 over | $ζ$ | $\geq$ 1 and contractions T acting on an n-dimensional Hilbert space, whose spectral…

math.CV2024

On the Fourier coefficients of powers of a finite Blaschke product

Alexander Borichev, Karine Fouchet, Rachid Zarouf

Given a finite Blaschke product $B$ we prove asymptotically sharp estimates on the $ℓ^{\infty}$ -norm of the sequence of the Fourier coefficients of $B^{n}$ as $n$ tends to $\inf…

math.CV2021

On the Fourier coefficients of powers of a Blaschke factor and strongly annular fonctions

Alexander Borichev, Karine Fouchet, Rachid Zarouf

We compute asymptotic formulas for the $k^{th}$ Fourier coefficients of $b_{λ}^{n}$ , where $b_{λ} (z) = \frac{z - λ}{1 - λ z}$ is the Blaschke factor associated to $λ \in D$ , $k\in[0,…