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Minimal projections onto subspaces generated by sign-matrices 符号矩阵生成的子空间上的最小投影
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-26 DOI: 10.1016/j.jat.2024.106084
Beata Derȩgowska , Barbara Lewandowska , Grzegorz Lewicki
{"title":"Minimal projections onto subspaces generated by sign-matrices","authors":"Beata Derȩgowska ,&nbsp;Barbara Lewandowska ,&nbsp;Grzegorz Lewicki","doi":"10.1016/j.jat.2024.106084","DOIUrl":"10.1016/j.jat.2024.106084","url":null,"abstract":"<div><p>The aim of this paper is to calculate relative and absolute projection constants of certain subspaces of <span><math><msubsup><mrow><mi>l</mi></mrow><mrow><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>l</mi></mrow><mrow><mi>∞</mi></mrow><mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msubsup></math></span> generated by eigenvectors of sign matrices. The main tool in our considerations is so called Chalmers–Metcalf operator (see Chalmers &amp; Metcalf (1994) and Lewicki &amp; Prophet (2021)). Also, some results from Castejon &amp; Lewicki (2014) and Castejon &amp; Lewicki (2019) will be applied.</p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"304 ","pages":"Article 106084"},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141846148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On approximation by rational functions in Musielak–Orlicz spaces 论穆西拉克-奥利兹空间中有理函数的逼近
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-26 DOI: 10.1016/j.jat.2024.106083
Wojciech M. Kozlowski , Gianluca Vinti
{"title":"On approximation by rational functions in Musielak–Orlicz spaces","authors":"Wojciech M. Kozlowski ,&nbsp;Gianluca Vinti","doi":"10.1016/j.jat.2024.106083","DOIUrl":"10.1016/j.jat.2024.106083","url":null,"abstract":"<div><p>We consider best approximation by rational functions in Musielak–Orlicz spaces of real-valued measurable functions over the unit interval equipped with the Lebesgue measure. We prove several properties of the respective multi-value projection operator, including its semi-continuity. Our results generalise known results for Lebesgue and variable Lebesgues spaces, and can be applied to special cases including Orlicz spaces and variable Lebesgue spaces with weights. We touch upon applications to image processing.</p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"304 ","pages":"Article 106083"},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021904524000716/pdfft?md5=772962309c292532c60924a31afa1fa7&pid=1-s2.0-S0021904524000716-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141847123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Machado–Bishop theorem in the uniform topology 统一拓扑中的马查多-毕夏普定理
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-26 DOI: 10.1016/j.jat.2024.106085
Deliang Chen
{"title":"The Machado–Bishop theorem in the uniform topology","authors":"Deliang Chen","doi":"10.1016/j.jat.2024.106085","DOIUrl":"10.1016/j.jat.2024.106085","url":null,"abstract":"<div><p>The Machado–Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado’s distance formula for bounded weighted vector-valued functions. A number of applications are given; in particular, some types of the Bishop–Stone–Weierstrass theorem for bounded vector-valued continuous spaces in the uniform topology are discussed; the splitting of <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>I</mi><mo>×</mo><mi>J</mi><mo>,</mo><mi>X</mi><mo>⊗</mo><mi>Y</mi><mo>)</mo></mrow></mrow></math></span> as the closure of <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>I</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mo>⊗</mo><mi>C</mi><mrow><mo>(</mo><mi>J</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow></mrow></math></span> in different senses and the extension of continuous vector-valued functions are studied.</p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"304 ","pages":"Article 106085"},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141848755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remembering Peter Benjamin Borwein (May 10, 1953–August 23, 2020) 缅怀彼得-本杰明-博文（1953 年 5 月 10 日-2020 年 8 月 23 日）
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-06 DOI: 10.1016/j.jat.2024.106070
Tamás Erdélyi
{"title":"Remembering Peter Benjamin Borwein (May 10, 1953–August 23, 2020)","authors":"Tamás Erdélyi","doi":"10.1016/j.jat.2024.106070","DOIUrl":"10.1016/j.jat.2024.106070","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106070"},"PeriodicalIF":0.9,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141700410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Peter Borwein: A philosopher’s mathematician 彼得-博文哲学家的数学家
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106071
David H. Bailey
{"title":"Peter Borwein: A philosopher’s mathematician","authors":"David H. Bailey","doi":"10.1016/j.jat.2024.106071","DOIUrl":"10.1016/j.jat.2024.106071","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106071"},"PeriodicalIF":0.9,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141690540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
In memory of Peter Borwein 纪念彼得-博尔文
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106072
Stephen Choi
{"title":"In memory of Peter Borwein","authors":"Stephen Choi","doi":"10.1016/j.jat.2024.106072","DOIUrl":"10.1016/j.jat.2024.106072","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106072"},"PeriodicalIF":0.9,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021904524000583/pdfft?md5=cbc6f03a9f2eb4bee6ad9cfdd54f3ec1&pid=1-s2.0-S0021904524000583-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141695786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
In memory of Peter Borwein 纪念彼得-博尔文
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106075
Boris Shekhtman
{"title":"In memory of Peter Borwein","authors":"Boris Shekhtman","doi":"10.1016/j.jat.2024.106075","DOIUrl":"10.1016/j.jat.2024.106075","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106075"},"PeriodicalIF":0.9,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141708036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remembering Peter Benjamin Borwein (May 10, 1953–August 23, 2020) 缅怀彼得-本杰明-博文（1953 年 5 月 10 日 - 2020 年 8 月 23 日）
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106073
Doron S. Lubinsky
{"title":"Remembering Peter Benjamin Borwein (May 10, 1953–August 23, 2020)","authors":"Doron S. Lubinsky","doi":"10.1016/j.jat.2024.106073","DOIUrl":"10.1016/j.jat.2024.106073","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106073"},"PeriodicalIF":0.9,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PII: S0021-9045(24)00055-8
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106069
Paul Nevai, Amos Ron
{"title":"","authors":"Paul Nevai,&nbsp;Amos Ron","doi":"10.1016/j.jat.2024.106069","DOIUrl":"10.1016/j.jat.2024.106069","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106069"},"PeriodicalIF":0.9,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
In Memoriam: Peter Benjamin Borwein (1953–2020) 悼念：彼得-本杰明-博文（1953-2020）
IF 0.9 3区 数学
Journal of Approximation Theory Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106074
Michael J. Mossinghoff
{"title":"In Memoriam: Peter Benjamin Borwein (1953–2020)","authors":"Michael J. Mossinghoff","doi":"10.1016/j.jat.2024.106074","DOIUrl":"10.1016/j.jat.2024.106074","url":null,"abstract":"<div><p>Peter Borwein had wide-ranging mathematical interests, and was a pioneer in computational and experimental investigations in many areas. We fondly recall some of his interests and contributions in a number of topics in analysis, number theory, and other areas, especially work where computation and experimentation played an important role. This includes his work on a number of extremal<span><span> problems regarding Littlewood polynomials and other families of integer polynomials with restricted coefficients, questions regarding the Mahler measure of an integer polynomial, problems on merit factors and Barker sequences, the Prouhet–Tarry–Escott problem, problems of Pólya and Turán regarding sums of the </span>Liouville function, and questions in combinatorial geometry regarding arrangements of points and lines.</span></p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"303 ","pages":"Article 106074"},"PeriodicalIF":0.9,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142040780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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