HILLE–YOSIDA AND STONE’S THEOREMS

This chapter is about the relation between \(\mathscr {C}^0\)-groups and their generators. In particular, we explain why to each unitary \(\mathscr {C}^0\)-group we may associate a unique self-adjoint operator. More importantly, we prove that any self-adjoint operator generates a unitary \(\mathscr {C}^0\)-group which solves an evolution equation, (e.g., the Schrodinger equation).