四元数多项式的零点:Eneström-Kakeya定理的推广

IF 0.4 4区数学 Q4 MATHEMATICS

Czechoslovak Mathematical Journal Pub Date : 2023-06-22 DOI:10.21136/CMJ.2023.0097-22

A. Mir

{"title":"四元数多项式的零点:Eneström-Kakeya定理的推广","authors":"A. Mir","doi":"10.21136/CMJ.2023.0097-22","DOIUrl":null,"url":null,"abstract":"We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"649 - 662"},"PeriodicalIF":0.4000,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem\",\"authors\":\"A. Mir\",\"doi\":\"10.21136/CMJ.2023.0097-22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.\",\"PeriodicalId\":50596,\"journal\":{\"name\":\"Czechoslovak Mathematical Journal\",\"volume\":\"73 1\",\"pages\":\"649 - 662\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Czechoslovak Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/CMJ.2023.0097-22\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/CMJ.2023.0097-22","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

给出了一类四元数变量正则多项式的零点位置的一些结果。利用新建立的正则函数与四元数变量多项式理论中的一个极大模定理和正则积的零集结构，导出了这些多项式的零的新的Eneström-Kakeya型界。我们的结果也将一些经典的结果从复数扩展到四元数。

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

On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem

We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.

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