双参数半群的预解算子

双参数半群的预解算子 ON THE RESOLVENT OPERATOR OF TWO-PARAMETER SEMI-GROUP 王志明 Wang Chiming first-author Hille-Yosida定理论述了线性算子族{R λ ,λ > 0)是某单参数半群的预解算子的充要条件。然而对于双参数的情形,并无相应的定理。本文证明了线性算子族{R λ, ;λ > 0,s≥0}在满足某种半时齐性的条件下是某双参数半群的右预解算子的充要条件。 Let be a Banach space, Rλ,8 is a linear operator from to , family {Rλ,8, λ>0, s≥0}is said to be semi-homogeneous, if lim Rλ,8 x exists, (λ>0, x∈. In this paper, we proved that a family of linear operator with semi-ho-mogeneous property {Rλ,8,λ>0, s≥0} can be the resolvent of some two-pa-rameter semi-group, then obtained the Hille-Yosida theorem for semi-homo-geneous two-parameter semi-group. 双参数半群 诱导半群 预解式 半时齐 强收敛 two-parameter semi-group induced semi-group resolvent semi-homogeneous strong convergence. 中国科学院科学基金 1988-03-01 2021-04-01 3