Construction of non-linear semi-groups using product formulas

Under certain circumstances, the Trotter-Lie formulaW _t=lim(U _t/nV_t/n) ⁿ is used to construct a non-linear semi-groupW _t on closed subsets ofL ^P, 1≦p<∞. In particular we consider the situation whereU _t=e ^tA is a positivity preservingC ₀ (linear) semi-group andV _t is generated by a (non-linear) functionF with certain monotonicity properties. In general,A andF are “singular” onL ^p and no requirement is made that one of them be “relatively bounded” with respect to the other. The generator of the resulting semi-groupW _t turns out to be an extension ofA +F restricted to a suitable domain. Research supported by a Danforth Graduate Fellowship and a Weizmann Postdoctoral Fellowship.