A continuous-parameter Katznelson-Tzafriri theorem for algebras of analytic functions

TL;DR

This paper extends the Katznelson-Tzafriri theorem to continuous parameters for power-bounded operators with bounded analytic Besov calculus, and further generalizes to operators with broader functional calculi.

Contribution

It introduces a continuous-parameter version of the Katznelson-Tzafriri theorem and extends it to operators with larger algebraic functional calculi.

Findings

Established a continuous-parameter Katznelson-Tzafriri theorem

Extended the theorem to operators with larger algebraic calculi

Applicable to a broader class of operators with analytic Besov functions

Abstract

We prove a continuous-parameter version of the recent theorem of Katznelson-Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We also show that the result can be extended to some operators which have functional calculi with respect to some larger algebras.