正则余弦算子函数的内插和外插定理

数学物理学报 ›› 1997, Vol. 17 ›› Issue (3): 294-300.

正则余弦算子函数的内插和外插定理

张寄洲^1,2

1 湖北大学数学系武汉 430062;
2 武汉大学数学系武汉 430072

收稿日期:1995-09-18 修回日期:1996-03-18 出版日期:1997-06-26 发布日期:1997-06-26
基金资助:
国家自然科学基金

Interpolation and Extrapolation Theorems of Regularized Cosine Operator Functions

Zhang Jizhou^1,2

1 Department of Mathematics, Hubei University, Whhan 430002;
2 Departmeat of Mathematics, Wuhan University, Wuhan 430072

Received:1995-09-18 Revised:1996-03-18 Online:1997-06-26 Published:1997-06-26

摘要/Abstract

摘要： 该文研究正则余弦算子函数的内插和外插.证明了线性算子A在Banach空间X中生成一个指数有界的C-正则余弦函数当且仅当存在Banach空间Y和线性算子B使得:[R(C)]→X→Y,这里C是C在Y中的有界扩张,B在Y中生成一个强连续余弦算子函数且A=B|_x.

关键词: 正则余弦函数, 积分余弦函数, 内插和外插

Abstract: In this paper, we study the interpolation and extrapolation theorems of regularized cosine operator funcitons. We show that the linear Operator a generates a exponentially bounded C -regularized cosine function on the Banach space X if and only if there exist a Banach space Y and a linear operator B such that:[R(C]→x→y, where C is a bounded extension of C on Y, B generates a strongly continuous cosine operator funciton and A=B|_x.

Key words: Regularized cosine function, Integrated cosine funcitons, Interpolation and extrapolation

张寄洲. 正则余弦算子函数的内插和外插定理[J]. 数学物理学报, 1997, 17(3): 294-300.

Zhang Jizhou. Interpolation and Extrapolation Theorems of Regularized Cosine Operator Functions[J]. Acta mathematica scientia,Series A, 1997, 17(3): 294-300.