关于维曼-瓦隆不等式的说明

arXiv - MATH - Complex Variables Pub Date : 2024-09-10 DOI:arxiv-2409.06499

Karl-G. Grosse-Erdmann

{"title":"关于维曼-瓦隆不等式的说明","authors":"Karl-G. Grosse-Erdmann","doi":"arxiv-2409.06499","DOIUrl":null,"url":null,"abstract":"The Wiman-Valiron inequality relates the maximum modulus of an analytic\nfunction to its Taylor coefficients via the maximum term. After a short\noverview of the known results, we obtain a general version of this inequality\nthat seems to have been overlooked in the literature so far. We end the paper\nwith an open problem.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"70 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on the Wiman-Valiron inequality\",\"authors\":\"Karl-G. Grosse-Erdmann\",\"doi\":\"arxiv-2409.06499\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Wiman-Valiron inequality relates the maximum modulus of an analytic\\nfunction to its Taylor coefficients via the maximum term. After a short\\noverview of the known results, we obtain a general version of this inequality\\nthat seems to have been overlooked in the literature so far. We end the paper\\nwith an open problem.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"70 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06499\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06499","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

Wiman-Valiron 不等式通过最大项将解析函数的最大模与其泰勒系数联系起来。在简要回顾了已知结果之后，我们得到了这个不等式的一般版本，而迄今为止，这个不等式似乎一直被文献所忽略。最后，我们以一个开放性问题结束本文。

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

A note on the Wiman-Valiron inequality

The Wiman-Valiron inequality relates the maximum modulus of an analytic function to its Taylor coefficients via the maximum term. After a short overview of the known results, we obtain a general version of this inequality that seems to have been overlooked in the literature so far. We end the paper with an open problem.

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

arXiv - MATH - Complex Variables

自引率

0.00%

发文量