局部有界双连续余弦算子函数的生成元及其性质

Generator and Properties of Locally Bounded Bi-Continuous Cosine Operator Functions

为了减弱余弦算子函数中的强连续性条件,把空间X约定到一个赋有范数拓扑(X,‖.‖)和局部凸拓扑(X,τ)的Banach空间上,又结合算子的局部有界性,引入了局部有界双连续函数的概念,并研究了其生成元及生成元的若干性质。

In order to relax the strong continuity properties of cosine operator functions,the spaces x is fixed to the Banach Spaces which is endowed with the norm topology and an locally convex topology.The concept of locally bounded Bi-continuous cosine operator functions is introduced combine with the locally bounded properties of operators.And the generator and sorne properties of local bounded bi-continuous cosine operator functions are investigated.