平面上的$C^{m}$半代数截面

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Mathematical Society of Japan Pub Date : 2021-01-16 DOI:10.2969/jmsj/86258625

C. Fefferman, Garving K. Luli

{"title":"平面上的$C^{m}$半代数截面","authors":"C. Fefferman, Garving K. Luli","doi":"10.2969/jmsj/86258625","DOIUrl":null,"url":null,"abstract":"for polynomials P1, · · · , Pr, Q1, · · · , Qs on R . (We allow the cases r = 0 or s = 0.) A semialgebraic function φ : E → R is a function whose graph {(x, φ(x)) : x ∈ E} is a semialgebraic set. We define smoothness in terms of C and C loc. Here, C m ( R,R ) denotes the space of all R-valued functions on R whose derivatives up to order m are continuous and bounded on R. C loc ( R,R ) denotes the space of R-valued functions on R with continuous derivatives up to order m. If D = 1, we write C (R) and C loc (R ) in place of C ( R,R )","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"$C^{m}$ semialgebraic sections over the plane\",\"authors\":\"C. Fefferman, Garving K. Luli\",\"doi\":\"10.2969/jmsj/86258625\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"for polynomials P1, · · · , Pr, Q1, · · · , Qs on R . (We allow the cases r = 0 or s = 0.) A semialgebraic function φ : E → R is a function whose graph {(x, φ(x)) : x ∈ E} is a semialgebraic set. We define smoothness in terms of C and C loc. Here, C m ( R,R ) denotes the space of all R-valued functions on R whose derivatives up to order m are continuous and bounded on R. C loc ( R,R ) denotes the space of R-valued functions on R with continuous derivatives up to order m. If D = 1, we write C (R) and C loc (R ) in place of C ( R,R )\",\"PeriodicalId\":49988,\"journal\":{\"name\":\"Journal of the Mathematical Society of Japan\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Mathematical Society of Japan\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2969/jmsj/86258625\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Mathematical Society of Japan","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2969/jmsj/86258625","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 6

摘要

对于R上的多项式P1，···，Pr，Q1，··，Qs。（我们允许r＝0或s＝0的情况。）半代数函数φ：E→ R是一个函数，其图{（x，φ（x））:x∈E}是半代数集。我们用C和C位置来定义光滑度。这里，Cm（R，R）表示R上所有R值函数的空间，其直到m阶的导数是连续的并且在R上有界。Cloc

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

$C^{m}$ semialgebraic sections over the plane

for polynomials P1, · · · , Pr, Q1, · · · , Qs on R . (We allow the cases r = 0 or s = 0.) A semialgebraic function φ : E → R is a function whose graph {(x, φ(x)) : x ∈ E} is a semialgebraic set. We define smoothness in terms of C and C loc. Here, C m ( R,R ) denotes the space of all R-valued functions on R whose derivatives up to order m are continuous and bounded on R. C loc ( R,R ) denotes the space of R-valued functions on R with continuous derivatives up to order m. If D = 1, we write C (R) and C loc (R ) in place of C ( R,R )

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the Mathematical Society of Japan 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).