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Title: Schroedinger operators with Rudin-Shapiro potentials are not palindromic

Abstract

We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. {bold 174}, 149{endash}159 (1995)] by showing that the Rudin-Shapiro sequence is not {ital palindromic}, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. {copyright} {ital 1997 American Institute of Physics.}

Authors:
 [1]
  1. CNRS, LRI, Batiment 490, F-91405 Orsay Cedex (France)
Publication Date:
OSTI Identifier:
527841
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 38; Journal Issue: 4; Other Information: PBD: Apr 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; QUANTUM OPERATORS; SCHROEDINGER PICTURE; MATHEMATICAL OPERATORS; POTENTIALS; SPECTRA; QUANTUM MECHANICS

Citation Formats

Allouche, J. Schroedinger operators with Rudin-Shapiro potentials are not palindromic. United States: N. p., 1997. Web. doi:10.1063/1.531916.
Allouche, J. Schroedinger operators with Rudin-Shapiro potentials are not palindromic. United States. https://doi.org/10.1063/1.531916
Allouche, J. 1997. "Schroedinger operators with Rudin-Shapiro potentials are not palindromic". United States. https://doi.org/10.1063/1.531916.
@article{osti_527841,
title = {Schroedinger operators with Rudin-Shapiro potentials are not palindromic},
author = {Allouche, J},
abstractNote = {We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. {bold 174}, 149{endash}159 (1995)] by showing that the Rudin-Shapiro sequence is not {ital palindromic}, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. {copyright} {ital 1997 American Institute of Physics.}},
doi = {10.1063/1.531916},
url = {https://www.osti.gov/biblio/527841}, journal = {Journal of Mathematical Physics},
number = 4,
volume = 38,
place = {United States},
year = {Tue Apr 01 00:00:00 EST 1997},
month = {Tue Apr 01 00:00:00 EST 1997}
}