ABSTRACT
We define new spaces of test functions and distributions admitting a Laplace transform in the classical sense, i.e. by evaluation at exponentials. We use these spaces to give a characterization of the Laplace inverses of analytic functions which are polynomially bounded on logarithmic regions and have values in a Banach space. As an illustration we give a conceptually new proof of the characterization of tempered convolution operators that have a distributional fundamental solution. Connections to asymptotic Lapalce transforms and Laplace transforms of (Laplace) hyperfunctions are sketched.
AMS Subject Classification: 44 A 10, 46 F 05, 44 A 35.
