Spectra of Stationary Processes on \(\mathbb{Z}\)

  • Alexander Borichev
  • Mikhail Sodin
  • Benjamin Weiss
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)


We will discuss a somewhat striking spectral property of finitely valued stationary processes on \(\mathbb{Z}\) that says that if the spectral measure of the process has a gap then the process is periodic. We will give some extensions of this result and raise several related questions.


Spectral measure spectrum finitely valued stationary process Carleman spectrum spectral set 

Mathematics Subject Classification (2010)

Primary 60G10. Secondary 30D99 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Borichev
    • 1
  • Mikhail Sodin
    • 2
  • Benjamin Weiss
    • 3
  1. 1.Aix-Marseille Université, CNRSCentrale Marseille, I2MMarseilleFrance
  2. 2.School of MathematicsTel Aviv UniversityTel AvivIsrael
  3. 3.Institute of MathematicsHebrew University of JerusalemJerusalemIsrael

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