A First Szegő’s Limit Theorem for a Class of Non-Toeplitz Matrices

详细信息    查看全文

• 作者：A. Bourget ; T. McMillen
• 关键词：First Szegő’s limit theorem ; Kac–Murdock–Szegő matrices ; Vanishing mean variation ; Equidistributed sequences
• 刊名：Constructive Approximation
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：45
• 期：1
• 页码：47-63
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Analysis;
• 出版者：Springer US
• ISSN：1432-0940
• 卷排序：45

文摘

We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are \(\mu \)-distributed for some probability measure. As an application of our results, we extend the well-known class of Kac–Murdock–Szegő  generalized Toeplitz matrices to sequences of matrices whose diagonal entries are modeled by Riemann integrable functions.