Spectral Homogeneity of Limit-Periodic Schr\"odinger Operators

Jake Fillman; Milivoje Lukic

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arXiv · 1502.05454

Spectral Homogeneity of Limit-Periodic Schr\"odinger Operators

Jake Fillman·Milivoje Lukic

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Abstract

We prove that the spectrum of a limit-periodic Schr\"odinger operator is homogeneous in the sense of Carleson whenever the potential obeys the Pastur--Tkachenko condition. This implies that a dense set of limit-periodic Schr\"odinger operators have purely absolutely continuous spectrum supported on a homogeneous Cantor set. When combined with work of Gesztesy--Yuditskii, this also implies that the spectrum of a Pastur--Tkachenko potential has infinite gap length whenever the potential fails to be uniformly almost periodic.

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Jake Fillman, Milivoje Lukic. 2015-02-19. Spectral Homogeneity of Limit-Periodic Schr\"odinger Operators. https://arxiv.org/abs/1502.05454

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