A Laplace transform relevant to holomorphic semigroups

Synopsis A Laplace transform is developed for functions which are holomorphic in the complex wedge Ω = { z | |arg ( z )| < σ}, where 0 ≦ σ < π. The resulting transform will be holomorphic in a complementary wedge of the form Ω a = { a + z ||arg ( z )|< (π/2) +σ for some a . This Laplace transform is shown to be an isomorphism between two appropriate spaces. The spanning properties of sets of the form { e λ k S }k∊I in the domain space are studied. These results are then applied to a control problem.