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The Spectrum of Periodic Jacobi Matrices with Slowly Oscillating Diagonal Terms

Published online by Cambridge University Press:  12 December 2008

Carmen Martíinez
Carmen Martíinez
Affiliation:
Departamento de Matemáaticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico City 04510, Mexico (cmai@lya.fciencias.unam.mx)
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Abstract

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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.

Keywords

Jacobi matricesorthogonal polynomialsspectrum
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