A complete theory for jointly continuous nonlinear semigroups on a complete separable metric space

Abstract

For a jointly continuous semigroup of transformations on a complete separable metric space X an induced semigroup of linear transformations on an appropriate space of measures is defined. A complete characterization of generators of such semigroups is given and it is shown how to construct a jointly continuous semigroup on X from a generator taken from this characterized collection.

Keywords:

• Nonlinear semigroup
• Generator
• Exponential formula

1991 Mathematic Subject Classifications:

• 47H20
• 58D07

^*To Robert Carroll. jwnunt.edu

^*To Robert Carroll. jwnunt.edu

Notes

^*To Robert Carroll. jwnunt.edu