A Formula representing magnetic Berezin transforms on the Bergman ball of ${\text{C}}^n$ as functions of the Laplace-Beltrami operator

We give a formula that represents magnetic Berezin transforms associated with generalized Bergman spaces as functions of the Laplace-Beltrami operator on the Bergman ball. In particular, we recover the result obtained by J. Peeter [J. Oper. Theory, 24, 1990].