Limit-periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum
نویسندگان
چکیده
We consider Schrödinger operators on the real line with limitperiodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral measures are purely singular continuous. Moreover, we show that for a dense set of limit-periodic potentials, the spectrum of the associated Schrödinger operator has Hausdorff dimension zero. In both results one can introduce a coupling constant λ ∈ (0,∞), and the respective statement then holds simultaneously for all values of the coupling constant. MSC2010 Subject Class: 34L40
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تاریخ انتشار 2016