Functional calculus estimates for Tadmor–Ritt operators

Abstract

ABSTRACT. We show H ∞ -functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor-Ritt operators in terms of the constant dependence. Furthermore, it is shown how discrete square function estimates influence the estimates.

On measuring unboundedness of the H∞-calculus for generators of analytic semigroups

“…It seems natural to use discrete versions of the techniques used in this paper to improve these results. Such results were recently obtained by the author, [34].…”

“…It seems natural to use discrete versions of the techniques used in this paper to improve these results. Such results were recently obtained by the author, [34]. We point out that in Theorems 2.3 and 2.10 the operator A need not be densely defined.…”

Remarks on Ritt operators, their $H^\infty$ functional calculus and associated square function estimates

“…Ritt -or Ritt-Tadmor -operators and their functional calculus have attracted some attention in recent years, see for example [1,2,4,5,8,14,17,19,21,24,26]. It is well known that the boundedness of the H ∞ functional calculus of sectorial or strip-type operators is linked to certain square function estimates, see for example [15,18,20], as well as [10,12] for extensive references.…”

R-boundedness

“…holds. This result was extended to Ritt operators on general Banach spaces by Schwenninger [2016b]. In such results, the role of sectors is taken by Stolz domains.…”