勘误:无界谱的Toeplitz积函数的误差界和渐近展开式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-08 DOI:10.1111/jtsa.12690

Tetsuya Takabatake

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引用次数: 1

摘要

我们研究了由在原点处有一些奇点的可积分函数在 [ - π , π ] 上生成的托普利兹矩阵乘积迹的积分极限近似的误差阶数。尽管 Lieberman 和 Phillips（2004 年，《时间序列分析杂志》，25(5) 733-753）的定理 2 中推导出了上述近似值的尖锐误差阶，但其证明存在不准确之处。在本文中，我们重新研究了上述迹近似问题的误差阶次，并严格验证了 Lieberman 和 Phillips (2004, Journal of Time Series Analysis, 25(5) 733-753) 中推导出的尖锐误差阶次。

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Corrigendum: Error bounds and asymptotic expansions for Toeplitz product functionals of unbounded spectra

We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on $[- π, π]$ 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).

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.