On the measure of gaps and spectra for discrete 1D Schrödinger operators

Y. Last*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

We study the lebesgue measure of gaps and spectra, of ergodic Jacobi matrices. We show that: |σ/A|+|G|≥v, where: σ is the spectrum, G is the union of the gaps, A is the set of energies where the Lyaponov exponent vanishes and v is an appropriate seminorm of the potential. We also study in more detail periodic Jacobi matrices, and obtain a lower bound and large coupling asymptotics for the measure of the spectrum. We apply the results of the periodic case, to limit periodic Jacobi matrices, and obtain sufficient conditions for |G|≥v and for |σ|>0.

Original languageAmerican English
Pages (from-to)347-360
Number of pages14
JournalCommunications in Mathematical Physics
Volume149
Issue number2
DOIs
StatePublished - Oct 1992
Externally publishedYes

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