PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE SQ(T) (1≤Q≤∞)

doi:10.1016/S0252-9602(15)60017-0

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 495-507.doi: 10.1016/S0252-9602(15)60017-0

PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T) (1≤Q≤∞)

徐艳艳¹, 陈广贵², 甘莹², 许燕²

1. Lab of Security Insurance of Cyberspace of Sichuan Province, School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China;
2. School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China

收稿日期:2014-02-19 修回日期:2014-09-26 出版日期:2015-03-20 发布日期:2015-03-20
通讯作者: Guanggui CHEN School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China E-mail: ggchen@mail.xhu.edu.cn; 919454185@qq.com; xuyan345@163.com E-mail:ggchen@mail.xhu.edu.cn;919454185@qq.com;xuyan345@163.com
基金资助:
This work is partially supported by National Nature Science Foundation of China (61372187), Sichuan Key Technology Research and Development Program (2012GZ0019, 2013GXZ0155), and the Fund of Lab of Security Insurance of Cyberspace, Sichuan Province (szjj2014-079).

PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T) (1≤Q≤∞)

Yanyan XU¹, Guanggui CHEN², Ying GAN², Yan XU²

1. Lab of Security Insurance of Cyberspace of Sichuan Province, School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China;
2. School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China

Received:2014-02-19 Revised:2014-09-26 Online:2015-03-20 Published:2015-03-20
Contact: Guanggui CHEN School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China E-mail: ggchen@mail.xhu.edu.cn; 919454185@qq.com; xuyan345@163.com E-mail:ggchen@mail.xhu.edu.cn;919454185@qq.com;xuyan345@163.com
Supported by:
This work is partially supported by National Nature Science Foundation of China (61372187), Sichuan Key Technology Research and Development Program (2012GZ0019, 2013GXZ0155), and the Fund of Lab of Security Insurance of Cyberspace, Sichuan Province (szjj2014-079).

摘要/Abstract

摘要：

Probabilistic linear (N, δ)-widths and p-average linear N-widths of Sobolev space W₂^r(T), equipped with a Gaussian probability measure μ, are studied in the metric of S_q(T) (1 ≤ q ≤ ∞), and determined the asymptotic equalities:

and

where 0< p <∞, δ∈ (0, 1/2 ], ρ >1, and S_q(T) is a subspace of S₁(T), in which the Fourier series is absolutely convergent in ?_q sense.

关键词: Probabilistic linear width, Average linear width, Gaussian measure, Sobolev space, linear operator

Abstract:

Key words: Probabilistic linear width, Average linear width, Gaussian measure, Sobolev space, linear operator

中图分类号:

41A46

徐艳艳, 陈广贵, 甘莹, 许燕. PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T) (1≤Q≤∞)[J]. 数学物理学报(英文版), 2015, 35(2): 495-507.

Yanyan XU, Guanggui CHEN, Ying GAN, Yan XU. PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T) (1≤Q≤∞)[J]. Acta mathematica scientia,Series B, 2015, 35(2): 495-507.

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PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T) (1≤Q≤∞)

PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T) (1≤Q≤∞)

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