33 citations · 106 across the 18 of their papers we have counts for
18 papers
Some developments around the Katznelson-Tzafriri theorem
Charles Batty, David Seifert
This paper is a survey article on developments arising from a theorem proved by Katznelson and Tzafriri in 1986 showing that if is a power-b…
A continuous-parameter Katznelson-Tzafriri theorem for algebras of analytic functions
Charles Batty, David Seifert
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…
Bounded functional calculi for unbounded operators
Charles Batty, Alexander Gomilko, Yuri Tomilov
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (ne…
A Katznelson-Tzafriri theorem for analytic Besov functions of operators
Charles Batty, David Seifert
Let be a power-bounded operator on a Banach space , be a Banach algebra of bounded holomorphic functions on the unit disc , and assume that there i…
Functional calculi for sectorial operators and related function theory
Charles Batty, Alexander Gomilko, Yuri Tomilov
We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of…
Besov spaces associated with non-negative operators on Banach spaces
Charles Batty, Chuang Chen
Motivated by a variety of representations of fractional powers of operators, we develop the theory of abstract Besov spaces for non-negative operators on…