Acta mathematica scientia, Series B >
PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE SQ(T) (1≤Q≤∞)
Received date: 2014-02-19
Revised date: 2014-09-26
Online published: 2015-03-20
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).
Probabilistic linear (N, δ)-widths and p-average linear N-widths of Sobolev space W2r(T), equipped with a Gaussian probability measure μ, are studied in the metric of Sq(T) (1 ≤ q ≤ ∞), and determined the asymptotic equalities:
and
where 0< p <∞, δ∈ (0, 1/2 ], ρ >1, and Sq(T) is a subspace of S1(T), in which the Fourier series is absolutely convergent in ?q sense.
Yanyan XU , Guanggui CHEN , Ying GAN , Yan XU . PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE SQ(T) (1≤Q≤∞)[J]. Acta mathematica scientia, Series B, 2015 , 35(2) : 495 -507 . DOI: 10.1016/S0252-9602(15)60017-0
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