Approximation by Convolution Translation Networks on Conic Domains  

作　　者：Bao Huai SHENG Dao Hong XIANG 

机构地区：[1]Department of Economic Statistics,School of International Business,Zhejiang Yuexiu University,Shaoxing,312000,P.R.China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua,321004,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第12期3127-3150,共24页数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.61877039);the NSFC/RGC Joint Research Scheme(Grant Nos.12061160462 and N_CityU102/20)of China;supported by the National Natural Science Foundation of China(Grant No.12471487);the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY23A010009)。

摘　　要：We give investigations on the approximation order of translation networks produced by the convolution translation operators defined on a Jacobi cone and the surface cone.We deal with the convolution translation from the view of Fourier analysis,express the translation operator with orthogonal basis and provide a sufficient condition to ensure the density for the translation networks.Based on these facts,we construct with the near best approximation operator and the Gauss integral formula two kinds of translation network operators and show their approximation orders in the best polynomial approximation.

关 键 词：Fourier orthogonal series conic domain localized kernel translation network density approximation order 

分 类 号：O177[理学—数学]