{"title":"Bernstein Inequality for the Riesz Derivative of Fractional Order Less Than Unity of Entire Functions of Exponential Type","authors":"A. O. Leont’eva","doi":"10.1134/S1064562423701491","DOIUrl":null,"url":null,"abstract":"<p>We consider Bernstein inequality for the Riesz derivative of order <span>\\(0 < \\alpha < 1\\)</span> of entire function of exponential type in the uniform norm on the real line. The interpolation formula is obtained for this operator; this formula has non-equidistant nodes. By means of this formula, the exact Bernstein inequality is found for all <span>\\(0 < \\alpha < 1\\)</span>, namely, the extremal entire function and the sharp constant are written out.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"108 3","pages":"524 - 527"},"PeriodicalIF":0.6000,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562423701491","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider Bernstein inequality for the Riesz derivative of order \(0 < \alpha < 1\) of entire function of exponential type in the uniform norm on the real line. The interpolation formula is obtained for this operator; this formula has non-equidistant nodes. By means of this formula, the exact Bernstein inequality is found for all \(0 < \alpha < 1\), namely, the extremal entire function and the sharp constant are written out.
Abstract We consider Bernstein inequality for the Riesz derivative of order \(0 < \alpha < 1\) of entire function of exponential type in the uniform norm on the real line.可以得到这个算子的插值公式；这个公式有非等距节点。通过这个公式，找到了所有 \(0 < \alpha < 1\) 的精确伯恩斯坦不等式，即写出了极值整个函数和锐常数。
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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