{"title":"切比雪夫基下多项式乘法器序列的奇偶性","authors":"Andrzej Piotrowski, Joshua Shterenberg","doi":"10.2140/involve.2023.16.689","DOIUrl":null,"url":null,"abstract":"We demonstrate that if $p\\in\\mathbb{R}[x]$ and $p$ is not an even function, then $\\{p(k)\\}^{\\infty}_{k=0}$ is not a multiplier sequence for the basis of Chebyshev polynomials of the first kind. We also give a characterization of geometric multiplier sequences for the Chebyshev basis.","PeriodicalId":36396,"journal":{"name":"Involve","volume":"1 4","pages":"0"},"PeriodicalIF":0.2000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Parity of polynomial multiplier sequences for the Chebyshev basis\",\"authors\":\"Andrzej Piotrowski, Joshua Shterenberg\",\"doi\":\"10.2140/involve.2023.16.689\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We demonstrate that if $p\\\\in\\\\mathbb{R}[x]$ and $p$ is not an even function, then $\\\\{p(k)\\\\}^{\\\\infty}_{k=0}$ is not a multiplier sequence for the basis of Chebyshev polynomials of the first kind. We also give a characterization of geometric multiplier sequences for the Chebyshev basis.\",\"PeriodicalId\":36396,\"journal\":{\"name\":\"Involve\",\"volume\":\"1 4\",\"pages\":\"0\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Involve\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/involve.2023.16.689\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Involve","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/involve.2023.16.689","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Parity of polynomial multiplier sequences for the Chebyshev basis
We demonstrate that if $p\in\mathbb{R}[x]$ and $p$ is not an even function, then $\{p(k)\}^{\infty}_{k=0}$ is not a multiplier sequence for the basis of Chebyshev polynomials of the first kind. We also give a characterization of geometric multiplier sequences for the Chebyshev basis.
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