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This paper investigates analytic Besov functions of n variables which act on the generators of n commuting C₀ -semigroups on a Banach space. The theory for n=1 has already been published, and the present paper uses a different approach to that case as well as extending to the cases when n2. It also clarifies some spectral mapping properties and provides some operator norm estimates.
Batty et al. (Thu,) studied this question.