{"title":"On the approximation of functions of several variables","authors":"B. Mond, O. Shisha","doi":"10.6028/JRES.070B.019","DOIUrl":null,"url":null,"abstract":"1. The purpose of this note is to point out how a certain type of approximation to fun ctions of one real variable, gives rise to similar approximations to functions of several variables. In fact, we show how information on the rapidity of cOQvergence of the approximation in the one dimensional case, yields at once corresponding information for the multidimensional case. 2. Let -oo < a < b <oo, and for n=l, 2, . .. , let c~,), cln), . •• , c\\!') be points of [a, b], and Kbn)(X), K\\n)(x), ... , K~n)(x) polynomials which are ;;:z,: ° throughout [a , b], and such that","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1966-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/JRES.070B.019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
1. The purpose of this note is to point out how a certain type of approximation to fun ctions of one real variable, gives rise to similar approximations to functions of several variables. In fact, we show how information on the rapidity of cOQvergence of the approximation in the one dimensional case, yields at once corresponding information for the multidimensional case. 2. Let -oo < a < b