Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case

Serguei Naboko; Sergey Simonov

doi:10.1017/S001309150700106X

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic (‘double root’) situation. For the model with ‘non-smooth’ matrix entries we obtain the asymptotics of generalized eigenvectors and analyse the spectrum. In addition, we reformulate a very helpful theorem from a paper by Janas and Moszynski in its full generality in order to serve the needs of our method.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Janas, J. and Naboko, S. 2013. ESTIMATES OF GENERALIZED EIGENVECTORS OF HERMITIAN JACOBI MATRICES WITH A GAP IN THE ESSENTIAL SPECTRUM. Mathematika, Vol. 59, Issue. 1, p. 191.

Moszyński, Marcin 2013. Non-Existence of Subordinate Solutions for Jacobi Operators in Some Critical Cases. Integral Equations and Operator Theory, Vol. 75, Issue. 3, p. 363.

Motyka, Wojciech 2014. Self-adjoint second-order difference equations with unbounded coefficients in the double root case. Journal of Difference Equations and Applications, Vol. 20, Issue. 3, p. 438.

Aptekarev, A.I. and Geronimo, J.S. 2016. Measures for orthogonal polynomials with unbounded recurrence coefficients. Journal of Approximation Theory, Vol. 207, Issue. , p. 339.

Kupin, S. and Naboko, S. 2018. On the Instability of the Essential Spectrum for Block Jacobi Matrices. Constructive Approximation, Vol. 48, Issue. 3, p. 473.

Janas, Jan Naboko, Sergey and Silva, Luis O. 2018. Green Matrix Estimates of Block Jacobi Matrices I: Unbounded Gap in the Essential Spectrum. Integral Equations and Operator Theory, Vol. 90, Issue. 4,

Świderski, Grzegorz 2018. Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime. Journal of Approximation Theory, Vol. 233, Issue. , p. 1.

Janas, Jan Naboko, Sergey and Silva, Luis O. 2020. Green Matrix Estimates of Block Jacobi Matrices II: Bounded Gap in the Essential Spectrum. Integral Equations and Operator Theory, Vol. 92, Issue. 3,

Świderski, Grzegorz and Trojan, Bartosz 2021. Asymptotic behavior of Christoffel–Darboux kernel via three-term recurrence relation II. Journal of Approximation Theory, Vol. 261, Issue. , p. 105496.

Naboko, Sergei Nikolaevich and Simonov, Sergey Aleksandrovich 2021. Формула Вейля-Титчмарша для спектральной плотности класса матриц Якоби в критическом случае. Функциональный анализ и его приложения, Vol. 55, Issue. 2, p. 21.

Naboko, S. N. and Simonov, S. A. 2021. Titchmarsh–Weyl Formula for the Spectral Density of a Class of Jacobi Matrices in the Critical Case. Functional Analysis and Its Applications, Vol. 55, Issue. 2, p. 94.

Świderski, Grzegorz and Trojan, Bartosz 2022. About essential spectra of unbounded Jacobi matrices. Journal of Approximation Theory, Vol. 278, Issue. , p. 105746.

Świderski, Grzegorz and Trojan, Bartosz 2023. Orthogonal Polynomials with Periodically Modulated Recurrence Coefficients in the Jordan Block Case II. Constructive Approximation, Vol. 58, Issue. 3, p. 615.

Silva, Luis O. and Simonov, Sergey 2023. From Complex Analysis to Operator Theory: A Panorama. Vol. 291, Issue. , p. 49.

Świderski, Grzegorz and Trojan, Bartosz 2024. Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case. Annales de l'Institut Fourier, Vol. 74, Issue. 4, p. 1521.

Naboko, S. and Simonov, S. 2024. Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices. St. Petersburg Mathematical Journal, Vol. 35, Issue. 1, p. 185.

Article contents

Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case

Abstract

Keywords

MSC classification

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case

Abstract

Keywords

MSC classification

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests