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Homogeneous Spectrum for Limit-Periodic Operators

Friday 10th April 2015 - 16:00 to 16:25
INI Seminar Room 1
Co-author: Milivoje Lukic (University of Toronto)

We will discuss the spectra of limit-periodic Schr\"odinger operators. Specifically, the spectrum of a limit-periodic operator which obeys the Pastur-Tkachenko condition is homogeneous in the sense of Carleson. When combined with work of Gesztesy-Yuditskii, our theorem implies that the spectrum of a continuum Schr\"odinger operator with Pastur--Tkachenko potential has infinite gap length whenever the potential fails to be uniformly almost periodic.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons