CONTINUOUS CONVOLUTION HEMIGROUPS
INTEGRATING A SUBMULTIPLICATIVE FUNCTION
Abstract: Unifying and generalizing previous investigations for vector spaces and for locally
compact groups, E. Siebert obtained the following remarkable result: A Lévy process on a
completely metrizable topological group 
, resp. a continuous convolution semigroup
of probabilities, satisfies a moment condition 
for some
submultiplicative function 
if and only if the jump measure of the process, resp. the
Lévy measure 
of the continuous convolution semigroup, satisfies 
for
some neighbourhood 
of the unit 
. Here we generalize this result to additive processes,
resp. convolution hemigroups 
, on (second countable) locally compact groups.
2000 AMS Mathematics Subject Classification: Primary: 60B15; Secondary: 60G51,
43A05, 47D06.
Keywords and phrases: Additive processes, convolution hemigroups, moment
conditions, submultiplicative functions, operator hemigroups, evolution families.
