On a class of one-parameter operator semigroups with state space Rn x Zm generated by pseudo-differential operators.

"The thesis shows that, under suitable conditions, a pseudo-differential operator, defined on some "nice" set of functions on Rn x Zm, with continuous negative definite symbol q(x,xi,o) extends to a generator of a Feller semigroup. Sections 1-5 are the preliminary sections, these sections discuss some harmonic analysis concerning locally compact Abelian groups. The essence of this thesis are Sections 6-13, which deals with obtaining the estimates required for the fulfilment of the conditions of the Hille-Yosida-Ray theorem.