Laplace transform generation theorems and local Cauchy problems (Q1773492)

The author generalizes several known results such as the complex representation theorem and a representation theorem of Prüss. He obtains new Hille-Yosida-type theorems for local convoluted semigroups. The first step of the technique which is proposed in the paper is to give new criteria for deciding if a vector-valued function is a local Laplace transform. The second step is to apply the previous criteria to the theory of local Cauchy problems.