Abstract
Lipschitzian semigroup refers to a one-parameter semigroup of Lipschitz operators that is strongly continuous in the parameter. It contains C 0 -semigroup, nonlinear semigroup of contractions and uniformly k-Lipschitzian semigroup as special cases. In this paper, through developing a series of Lipschitz dual notions, we establish an analysis approach to Lipschitzian semigroup. It is mainly proved that a (nonlinear) Lipschitzian semigroup can be isometrically embedded into a certain C 0 -semigroup. As application results, two representation formulas of Lipschitzian semigroup are established, and many asymptotic properties of C 0 -semigroup are generalized to Lipschitzian semigroup.
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