Abstract We consider a Nevanlinna–Pick interpolation problem on finite sequences of the
unit disc DD constrained by Hardy and radial-weighted Bergman norms. We find sharp …

In 2005, N. Nikolski proved among other things that for any $ r\in (0, 1) $ and any $ K\geq 1$,
the condition number $ CN (T)=\Vert T\Vert\cdot\Vert T^{-1}\Vert $ of any invertible n …

Given a Hilbert space operator T, the level sets of function Ψ T (z)=‖(T− z)− 1‖− 1
determine the so-called pseudospectra of T. We set Ψ T to be zero on the spectrum of T …

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

We derive new estimates for distances between optimal matchings of eigenvalues of non-
normal matrices in terms of the norm of their difference. We introduce and estimate a …

We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc,
constrained by Beurling–Sobolev norms. We find sharp asymptotics of the corresponding …

This note surveys recent strategies to estimate the condition number CN (T)= ‖ T ‖ ⋅ ‖ T^-
1 ‖ CN (T)=‖ T‖·‖ T-1‖ of complex n * nn× n matrices T with given spectrum. More …