正则α-次预解族与积分α-次预解族(英文)

Regularizedα-times resolvent families and integratedα-times resolvent families

为研究不适定的抽象Cauchy问题,Da Prato引入了正则半群,而Arendt则引入了积分半群的概念.deLaubenfels给出了这两种半群之间的联系.本文将delaubenfels的上述结论推广到了正则α-次预解族和积分α-次预解族上.最后给出这个定理的一些简单推论.

Regularized semigroups and integrated semigroups are introduced by Da Prato and Arendt re-spectively,to treat Cauchy problems which are not well-posed.deLaubenfels have studied the relation-ship between these two different semigroups.We give the relations between regularizedα-times resolv-ent families and integratedα-times resolvent families,which generalizes the corresponding results for regularized semigroups and integrated semigroups given by deLaubenfels.In the end we give some corol-laries.