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The Spectrum of Periodic Jacobi Matrices with Slowly Oscillating Diagonal Terms
Published online by Cambridge University Press: 12 December 2008
Abstract
We study the spectrum of periodic Jacobi matrices. We concentrate on the case of slowly oscillating diagonal terms and study the behaviour of the zeros of the associated orthogonal polynomials in the spectral gap. We find precise estimates for the distance from single eigenvalues of truncated matrices in the spectral gap to the diagonal entries of the matrix. We include a brief numerical example to show the exactness of our estimates.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 3 , October 2008 , pp. 751 - 763
- Copyright
- Copyright © Edinburgh Mathematical Society 2008
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