Nonlinear functions and the norm of the propagators of operational equations
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We explore the relation between nonlinear functions and the norm functions of the propagators of operational equations in infinite-dimensional spaces. A general criterion is obtained to judge whether a given nonlinear function is the norm function of some C 0-semigroup, the propagator of a wellposed Cauchy problem for an operational equation in an infinite-dimensional space, which gives a solution to an open problem posed in Lin et al. (2010) . Moreover, applying our abstract results, we show the existence of two valuable C 0-semigroups, which one has been seeking. 2012 Elsevier B.V.