A characterization of potential kernels on the positive half-line

Abstract

The set P of potential kernels on the half-line [0, τ[ is characterized as the set of positive measures k on [0,τ[ for which the Laplace transform f=ℒk{cyrillic} has the property that the sequence {Mathematical expression} is proportional with a renewal sequence for each s>0. This is analogous to a characterization, due to F. Hirsch, of a convex cone H contained in P. The corresponding result for another convex cone S{subset double equals}H is also given. © 1978 Springer-Verlag.