A Banach algebra of generalized functions

An algebraic isomorphism from a convolution algebra of Laplace transformable functions with support on the half-line to a complete discrete normed convolution algebra of sequences is used to construct generalized functions. The extension of this function-to-sequence map to a commutative Banach algebra of generalized functions is shown to be a Banach algebra isomorphism which can be utilized to establish a discrete formulation of a Mikusiński-type operational calculus and to construct algorithms for the numerical solution of half-line convolution equations.