{"title":"Corrigendum: Error bounds and asymptotic expansions for Toeplitz product functionals of unbounded spectra","authors":"Tetsuya Takabatake","doi":"10.1111/jtsa.12690","DOIUrl":null,"url":null,"abstract":"<p>We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on <math>\n <mrow>\n <mo>[</mo>\n <mo>−</mo>\n <mi>π</mi>\n <mo>,</mo>\n <mi>π</mi>\n <mo>]</mo>\n </mrow></math> having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem 2 of Lieberman and Phillips (2004, <i>Journal of Time Series Analysis</i>, 25(5) 733–753), its proof contains an inaccuracy. In the present article, we reinvestigate error orders of the above trace approximation problem and rigorously validate the sharp error order derived in Lieberman and Phillips (2004, <i>Journal of Time Series Analysis</i>, 25(5) 733–753).</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12690","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/jtsa.12690","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem 2 of Lieberman and Phillips (2004, Journal of Time Series Analysis, 25(5) 733–753), its proof contains an inaccuracy. In the present article, we reinvestigate error orders of the above trace approximation problem and rigorously validate the sharp error order derived in Lieberman and Phillips (2004, Journal of Time Series Analysis, 25(5) 733–753).
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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