On Joint Functional Calculus for Ritt Operators

In this paper, we study joint functional calculus for commuting n -tuple of Ritt operators. We provide an equivalent characterisation of boundedness for joint functional calculus for Ritt operators on L p -spaces, 1 < p < ∞ , where each of them admits a bounded functional calculus. We also investigate joint similarity problem for commuting n -tuple of Ritt operators. We get our results by proving a suitable multivariable transfer principle between sectorial and Ritt operators as well as an appropriate joint dilation result in a general setting.