On discrete subordination of power bounded and Ritt operators

Abstract

By means of a new technique, we develop further a discrete subordination approach to the functional calculus of power bounded and Ritt operators initiated by N. Dungey in [19]. This allows us to show, in particular, that (infinite) convex combinations of powers of Ritt operators are Ritt. Moreover, we provide a unified framework for several main results on discrete subordination from [19] and answer a question left open in [19]. The paper can be considered as a complement to [26] for the discrete setting.

This is the authors accepted manuscript for a paper being published in Indiana Univ. Math. J

References in corpus (3)

• Product formulas in functional calculi for sectorial operators
• Resolvent representations for functions of sectorial operators
• On the Ritt property and weak type maximal inequalities for convolution powers on ${\ell }^1(\mathbb{Z})$