PC[0,1]的共轭空间
Conjugate Space of PC[0,1]
摘要:
本文基于连续函数空间的共轭空间的构造方法，通过Stieltjes积分理论，得到了区间上具有有限个间断点，在间断点处仅左连续且右极限存在的函数全体所成空间的共轭空间。随后给出区间上具有无限个间断点，在间断点处仅左连续且右极限存在的函数全体所成空间的共轭空间。
Abstract:
Based on the construction method of conjugate space of continuous function space and Stieltjes integral theory, this paper obtains the conjugate space of the PC[0,1] space in which the functions has finite discontinuous points, has right limit at discontinuity points and is left continuous at discontinuity points. Finally, we get conjugate space of the PC[0,1] space in which the functions has infinite discontinuous points, has right limit at discontinuity points and is left continuous at dis-continuity points also.
参考文献
|
[1]
|
郭大钧, 孙经先, 刘兆理. 非线性常微分方程中的泛函方法[M]. 济南: 山东科学技术出版社, 2005.
|
|
[2]
|
Lakshmikantham, V. and Simeonov, P.S. (1989) Theory of Impulsive Differential Equations. World Scien-tific Publishing Co Pte Ltd., Singapore.
[Google Scholar] [CrossRef]
|
|
[3]
|
Kalton, N.J., Peck, N.T. and Roberts, J.W. (1984) An F-Space Sampler. Cambridge University Press, London.
[Google Scholar] [CrossRef]
|
|
[4]
|
吕和祥, 王天明. 实用泛函分析[M]. 大连: 大连理工大学出版社, 2011.
|
|
[5]
|
周美柯. 泛函分析[M]. 北京: 北京师范大学出版社, 2011.
|
|
[6]
|
王文智, 康晓红. 基本巴拿赫空间[M]. 广州: 华南理工大学出版社, 2013.
|
|
[7]
|
李艳玲, 赵静. KlnK共轭空间的构造及其性质[J]. 河北工业大学学报, 2005, 34(4): 79-81.
|
|
[8]
|
王见勇. 几个ι0类赋准范空间的共轭空间的表示定理[J]. 数学学报, 2016, 59(4): 519-526.
|
|
[9]
|
向阳洁, 陈国贤, 罗先发. 一个赋范空间的完备化及共轭空间[J]. 吉首大学学报(自然科学版), 2006, 27(2): 25-27.
|
|
[10]
|
郭大钧, 黄春朝, 梁方豪, 韦忠礼. 实变函数与泛函分析[M]. 济南: 山东大学出版社, 2005.
|
|
[11]
|
何穗, 刘敏思. 实变函数[M]. 武汉: 华中师范大学出版社, 2013.
|