Notation and some preliminaries from analysis

Co[0, oo) is the space of the functions continuous on [0, oo) and such th a t f ( t ) -> 0 as t —> oo with the sup-norm.

if it is clear what segment is considered, then we write varcr(f). / * g is the convolution of the functions / and #, i.e.,

( f * g ) ( x ) = J f ( x - t ) g ( t ) d t , * £ R .