TY - JOUR

T1 - On the measure of gaps and spectra for discrete 1D Schrödinger operators

AU - Last, Y.

PY - 1992/10

Y1 - 1992/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21144477066&partnerID=8YFLogxK

U2 - 10.1007/BF02097629

DO - 10.1007/BF02097629

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AN - SCOPUS:21144477066

SN - 0010-3616

VL - 149

SP - 347

EP - 360

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -