Spectra of Stationary Processes on Z

Alexander Borichev (1) , Mikhail Sodin (2) , Benjamin Weiss (3)

1 I2M - Institut de Mathématiques de Marseille
2 TAU - School of Mathematical Sciences [Tel Aviv]
3 HUJ - The Hebrew University of Jerusalem

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.

Mots clés: Spectral measure; spectrum; finitely valued stationary process; Carleman spectrum; spectral set

Domaines: Probabilités [math.PR]; Analyse classique [math.CA]

Alexander Borichev, Mikhail Sodin, Benjamin Weiss. Spectra of Stationary Processes on Z. Baranov A., Kisliakov S., Nikolski N. 50 Years with Hardy Spaces (A Tribute to Victor Havin), 261, Springer, pp.141-157, 2018, Operator Theory: Advances and Applications, 978-3-319-59077-6. ⟨10.1007/978-3-319-59078-3_7⟩. ⟨hal-02090075⟩