赋Gauss测度的球上加权Sobolev空间中Gel'fand型逼近特征  

Approximation Characteristics of Gel'fand Type in Weighted Sobolev Spaces on the Ball Equipped with Gaussian Measures

作　　者：刘禹祺 吴瑞欢 李冱岸[1] LIU Yuqi;WU Ruihuan;LI Hu'an(College of Science,North China University of Technology,Beijing,100144,P.R.China)

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《数学进展》2025年第1期113-122,共10页Advances in Mathematics(China)

基　　金：北方工业大学理学院院长基金(No.110051360022XN128)。

摘　　要：本文的主要工作是确定定义在欧氏球B^(d)上的加权Sobolev空间W_(2,μ)^(r)(B^(d))在加权q次Lebesgue可积函数空间L_(q,μ)(B^(d))尺度下概率与平均Gel'fand宽度的精确阶,其中权函数为1-‖x‖_(2)~2)^(μ-1/2),μ≥0,且在W_(2,μ)^(r)(B^(d))中赋以Gauss测度v.本文利用离散化方法得到了概率Gel'fand(n,δ)-宽度的结果,而后利用概率Gel'fand(n,δ)-宽度的结果以及实分析的方法得出了p-平均Gel'fand n-宽度的精确阶.The main work of this paper is to fix the sharp bounds of the probabilistic and the average Gel'fand width of the weighted Sobolev space W_(2,μ)~r(B~d)defined on the Euclidean ball B~d on the weighted qth Lebesgue integrable function space L_(2,μ)(B~d)scale,where the weight function is(1-‖x‖_(2)~2)^(μ-1/2),μ≥0,and the Gaussian measure v is equipped with the space W_(2,μ)~r(B~d).In this paper,using the discretization method,we obtain the results of the probabilistic Gel'fand(n,δ)-widths.Then,using the results of the probabilistic Gel'fand(n,δ)-widths and the method of real analysis,we obtain the sharp bounds of the p-average Gel'fand n-width.

关 键 词：概率宽度 平均宽度 加权SOBOLEV空间 GAUSS测度 

分 类 号：O174.41[理学—数学]