# On Functional Calculus For $n$-Ritt operators

## TL;DR

This paper introduces the class of $n$-Ritt operators, extending Ritt operators to a discrete setting, and develops a corresponding $H^$-functional calculus along with transference results and generalizations.

## Contribution

It defines $n$-Ritt operators, establishes their $H^$-functional calculus, and generalizes related concepts, providing new tools for discrete operator analysis.

## Key findings

- Introduction of $n$-Ritt operators as a discrete analogue of $n$-sectorial operators
- Development of an $H^$-functional calculus for $n$-Ritt operators
- Generalization of quadratic functional calculus and $n$-$R$-Ritt operators

## Abstract

In this paper, we present a new class of operators, which we name to be $n$-Ritt operators. This produces a discrete analogue of $n$-sectorial operators and generalizes the notion of Ritt operators. We develop a $H^\infty$-functional calculus for $n$-Ritt operators and prove an useful transference result. We also generalize the notions of quadratic functional calculus and $n$-$R$-Ritt operator and discuss some examples.