Iterates of the Bochner–Martinelli Integral Operator in a Ball

In the present paper we prove the convergence of iterates of the integral Bochner–Martinelli operator in a ball in various spaces: the infinitely-smooth functions, the analytic functions and the spaces conjugate to them, the distributions and the analytic functionals. We give a description of a spectrum of this operator in these spaces as well as the space $\mathcal L^p$.