ABSTRACT. We show that the product of commuting generators of polyno-mially bounded regularized groups generates a polynomially bounded reg-ularized group. We obtain similar results when one operator generates a bounded regularized semigroup and the other is the momentum of a spec-tral distribution. 0. Introduction. In this paper, we consider products of commuting generators of poly-nomially bounded strongly continuous groups, or more generally, regular-ized groups. It is a surprising fact that, even when both iA and iB generate commuting strongly continuous groups, and B is bounded, iBA may no

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