勘误:无界谱的Toeplitz积函数的误差界和渐近展开式

IF 1.2 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Time Series Analysis 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

Journal of Time Series Analysis 数学-数学跨学科应用

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： During the last 30 years Time Series Analysis has become one of the most important and widely used branches of Mathematical Statistics. Its fields of application range from neurophysiology to astrophysics and it covers such well-known areas as economic forecasting, study of biological data, control systems, signal processing and communications and vibrations engineering. The Journal of Time Series Analysis started in 1980, has since become the leading journal in its field, publishing papers on both fundamental theory and applications, as well as review papers dealing with recent advances in major areas of the subject and short communications on theoretical developments. The editorial board consists of many of the world''s leading experts in Time Series Analysis.