【摘要】 <正> 双参数算子半群概念是由于研究非时齐马氏过程产生的。由于它的复杂性,目前国内外对它的研究很少,文献不多,胡迪鹤教授在[1]中研究了双参数半群的连续性,可微性和拉氏变换,以及由转移函数产生的双参数半群的性质。本文在[1]的基础上,引进了双参数半群的诱导半群的概念,证明了双参数半群由其诱导半群的无穷小算子唯一确定,类似于Hille—Yosida 定理,对于给定的一族算子 R(?),给出了存在某双参数半群其诱导半群的预解算子族为 R(?)的充要条件。更多还原

【Abstract】 Let （?） be a Banach space.{T_s,t,0≤s≤t<∞} is a two-parameters constr-action semigroup on （?）.（?）^?is the set of all abstract functions （?）=x（·）de-fined on[0,∞) with vatues in （?）.（?）is a closed linear subspace.If a famity of bounded linear operators {T_t}（t≥0）on B is defined by（T_i（?））（s）=T_s,s+tx（s+t）,（?）is a semigrup on B.Then {T_t,t≥0} is said to be a induced semigroup of two-parameters semigroup {T_s,t,0≤s≤t<∞}.In this Paper,the relationships between two-parameters semigroup and its induced semigrosup are investegated.We proved that any two-parameters semi-group is determmted uniquely by the infinitesimal operator of its indued sem-ig oup,and that two-parameters semigroup can be described by the solutions of a equation,and obtainod The Hille-Yosida theorem for two-parameters semig-roup.更多还原