A Ritt-Kreiss condition: spectral localization and norm estimates

TL;DR

This paper introduces the $(eta, eta)$-RK condition, a generalization of Ritt and Kreiss operators, analyzing spectral properties, norm estimates, and applications to $L^p$ space interpolation.

Contribution

It generalizes Ritt and Kreiss operators through the $(eta, eta)$-RK condition, providing spectral analysis, norm estimates, and interpolation results.

Findings

Spectral localization for $eta<1$

Operators with $eta + eta=1$ are Ritt

Norm estimates for powers and differences

Abstract

A new condition is introduced by generalizing the Ritt and Kreiss operators named $(\alpha, \beta)$-RK condition. Geometrical properties of the spectrum for the case $\beta < 1$ are studied, moreover it is shown that in that case if $\alpha + \beta = 1$ the operator is Ritt. Estimates for the power and power differences norms for this type of operators are also studied. Lastly we apply this theory to obtain and interpolation result over Ritt and Kreiss operator on $L^p$ spaces.