Generalized Prüfer variables for perturbations of Jacobi and CMV matrices

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• 作者：Milivoje Lukic^a ; ^b ; ^{mlukic@math.toronto.edu" class="auth_mail" title="E-mail the corresponding author} ; Darren C. Ong^c ; ^{darrenong@xmu.edu.my" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Spectral theory ; Perturbation theory ; CMV operators ; Jacobi operators ; Prü ; fer variables
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：444
• 期：2
• 页码：1490-1514
• 全文大小：523 K

文摘

Prüfer variables are a standard tool in spectral theory, developed originally for perturbations of the free Schrödinger operator. We adapt the generalized Prüfer variables, introduced by Kiselev–Remling–Simon for perturbations of an arbitrary Schrödinger operator, to the setting of Jacobi and Szegő recursions. We present an application to random L²$L^2$ perturbations of Jacobi and CMV matrices, and an application to decaying oscillatory perturbations of periodic Jacobi and CMV matrices.