Zero measure spectrum for multi-frequency Schrodinger operators
Chaika J, Damanik D, Fillman J, Gohlke P (2022)
Journal of Spectral Theory 12(2): 573-590.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Chaika, Jon;
Damanik, David;
Fillman, Jake;
Gohlke, PhilippUniBi
Einrichtung
Abstract / Bemerkung
Building on works of Berthe-Steiner-Thuswaldner and Fogg-Nous, we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence, we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrodinger operator has Cantor spectrum of zero Lebesgue measure. We also describe a framework that can allow this to be extended to higher-dimensional tori.
Stichworte
Multifrequency quasiperiodic operators;
Cantor spectrum;
multidimensional continued fractions;
Schrodinger operators;
S-adic;
subshifts
Erscheinungsjahr
2022
Zeitschriftentitel
Journal of Spectral Theory
Band
12
Ausgabe
2
Seite(n)
573-590
ISSN
1664-039X
eISSN
1664-0403
Page URI
https://pub.uni-bielefeld.de/record/2967878
Zitieren
Chaika J, Damanik D, Fillman J, Gohlke P. Zero measure spectrum for multi-frequency Schrodinger operators. Journal of Spectral Theory. 2022;12(2):573-590.
Chaika, J., Damanik, D., Fillman, J., & Gohlke, P. (2022). Zero measure spectrum for multi-frequency Schrodinger operators. Journal of Spectral Theory, 12(2), 573-590. https://doi.org/10.4171/JST/411
Chaika, Jon, Damanik, David, Fillman, Jake, and Gohlke, Philipp. 2022. “Zero measure spectrum for multi-frequency Schrodinger operators”. Journal of Spectral Theory 12 (2): 573-590.
Chaika, J., Damanik, D., Fillman, J., and Gohlke, P. (2022). Zero measure spectrum for multi-frequency Schrodinger operators. Journal of Spectral Theory 12, 573-590.
Chaika, J., et al., 2022. Zero measure spectrum for multi-frequency Schrodinger operators. Journal of Spectral Theory, 12(2), p 573-590.
J. Chaika, et al., “Zero measure spectrum for multi-frequency Schrodinger operators”, Journal of Spectral Theory, vol. 12, 2022, pp. 573-590.
Chaika, J., Damanik, D., Fillman, J., Gohlke, P.: Zero measure spectrum for multi-frequency Schrodinger operators. Journal of Spectral Theory. 12, 573-590 (2022).
Chaika, Jon, Damanik, David, Fillman, Jake, and Gohlke, Philipp. “Zero measure spectrum for multi-frequency Schrodinger operators”. Journal of Spectral Theory 12.2 (2022): 573-590.
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