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

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

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 $[- π, π]$ 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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勘误:无界谱的Toeplitz积函数的误差界和渐近展开式

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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