The Absolutely Continuous Spectrum of the Almost Mathieu Operator
نویسنده
چکیده
We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon’s list of Schrödinger operator problems for the twenty-first century.
منابع مشابه
Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-critical Coupling
We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, settling the measure-theoretical case of Problem 6 of Barry Simon’s list of Schrödinger operator problems for the twenty-first century.
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