JournalsjstVol. 9, No. 4pp. 1223–1248

Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies

  • Wencai Liu

    University of California at Irvine, USA and Texas A&M University, College Station, USA

  • Yunfeng Shi

    Fudan University, Shanghai, China and Peking University, Beijing, China
Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies cover

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Abstract

We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schrödinger operators with Liouville frequencies decays exponentially. As an application, we obtain the homogeneity of the spectrum.

Cite this article

Wencai Liu, Yunfeng Shi, Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies. J. Spectr. Theory 9 (2019), no. 4, pp. 1223–1248

DOI 10.4171/JST/275