Spectra of stationary processes on Z

Alexander Borichev*, Mikhail Sodin, Benjamin Weiss

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We will discuss a somewhat striking spectral property of finitely valued stationary processes on 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.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Number of pages17
StatePublished - 2018

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


FundersFunder number
Horizon 2020 Framework Programme692616
Iowa Science Foundation382/15
European Research Council


    • Carleman spectrum
    • Finitely valued stationary process
    • Spectral measure
    • Spectral set
    • Spectrum


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