Convolution Operator Semi-Groups On L～1(D₂)

This paper mainly discusses convolution operator semigroups on L¹(D₂). It at first gives the general construction of such a semigroup {T_ut}_{t∈[0,∞}), proving that it becomes a semigroup iff there exists aα(w)∈R for each w∈W₂ such that (?)t(w)=e^α(w)t(t∈[0,∞)) and then giving its generator. In other sections different convolution operator semigroups are discussed. It shows in Section 5 that each Radon-Nikodym convolution opeator is compact and so there is no R-bounded Radon-Nikodym semigroup. Section 6 contributes to convolution operator semigroups generated by product measures are discussed. In Section 7 and Section 8 the Dunford-Pettis convolution operator semigroups and the Rosenthal convolution operator semigroups are discussed separately.