Uniform Spectral Properties of One-Dimensional Quasicrystals, III. α-Continuity
Uniform Spectral Properties of One-Dimensional Quasicrystals, III. α-Continuity
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DOI：
10.1007/s002200000203
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发表时间：
1999-10
影响因子：
2.4
通讯作者：
D. Damanik;R. Killip;D. Lenz
中科院分区：
文献类型：
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作者：
D. Damanik;R. Killip;D. Lenz
我们研究一维全线薛定谔算子的谱特性，特别是具有斯特米安势的算子。基于 Jitomirskaya——吉尔伯特-皮尔逊从属理论的最后扩展，我们演示了如何从半线上解的幂律界限建立全线算子的 α 连续性。然而，我们要求这些界限在边界条件下一致。我们能够用有界密度的旋转数和任意耦合常数来证明 Sturmian 势的这些界限。由此，我们为所有相统一建立纯α-连续谱。我们的分析还允许我们证明点谱对于所有斯特米亚势都是空的。
We study the spectral properties of one-dimensional whole-line Schrödinger operators, especially those with Sturmian potentials. Building upon the Jitomirskaya–Last extension of the Gilbert–Pearson theory of subordinacy, we demonstrate how to establish α-continuity of a whole-line operator from power-law bounds on the solutions on a half-line. However, we require that these bounds hold uniformly in the boundary condition.We are able to prove these bounds for Sturmian potentials with rotation numbers of bounded density and arbitrary coupling constant. From this we establish purely α-continuous spectrum uniformly for all phases.Our analysis also permits us to prove that the point spectrum is empty forallSturmian potentials.