Widder-Arendt theorem and integrated semigroups in locally convex space  

作　　者：肖体俊 梁进 

机构地区：[1]Department of Mathematics, Yunnan Teachers University, Kunming 650092, China [2]Teaching and Research Section of Mathematics, Kunming University of Science and Technology,Kunming 650093, China

出　　处：《Science China Mathematics》1996年第11期1121-1130,共10页中国科学：数学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China and the ABSF of Yunnan Province.

摘　　要：A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (Theorem 1.1). Moreover, integrated semigroups in such spaces are introduced and generation theorems and some basic properties for semigroups of this type are obtained. As examples, elliptic differential operators on certain classes of function spaces with locally convex topology are shown to be the generators of integrated semigroups under some conditions.A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (Theorem 1.1). Moreover, integrated semigroups in such spaces are introduced and generation theorems and some basic properties for semigroups of this type are obtained. As examples, elliptic differential operators on certain classes of function spaces with locally convex topology are shown to be the generators of integrated semigroups under some conditions.

关 键 词：LOCALLY CONVEX space Widder-Arendt THEOREM integrated SEMIGROUP ELLIPTIC differential operator. 

分 类 号：O152.7[理学—数学]