Purely Singular Continuous Spectrum for CMV Operators Generated by Subshifts

Abstract

We prove uniform absence of point spectrum for CMV operators corresponding to the period doubling subshift. We also prove almost sure absence of point spectrum for CMV operators corresponding to a class of Sturmian subshifts. Lastly, we prove almost sure absence of point spectrum for CMV operators corresponding to some subshifts generated by a coding of a rotation.

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Acknowledgments

I wish to thank David Damanik and Paul Munger for helpful conversations. I also wish to thank the anonymous referees for many useful suggestions, corrections and comments. The author was supported in part by NSF Grant DMS–1067988

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Correspondence to Darren C. Ong.

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Ong, D.C. Purely Singular Continuous Spectrum for CMV Operators Generated by Subshifts. J Stat Phys 155, 763–776 (2014). https://doi.org/10.1007/s10955-014-0974-2

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Keywords

  • Spectral Theory
  • Mathematical Physics
  • Dynamical Systems