Abstract
Let (G/Γ, Ra) be an ergodic k-step nilsystem for k ≥ 2. We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L2 (G/Γ) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multiplicity. In particular, we generalize a result previously established by Host–Kra–Maass [J. Anal. Math. 124 (2014), pp. 261–295] for 2-step nilsystems and a result by Stepin [Uspehi Mat. Nauk 24 (1969), pp. 241–242] for nilsystems G/Γ with connected, simply connected G.
Original language | English |
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Pages (from-to) | 469-480 |
Number of pages | 12 |
Journal | Proceedings of the American Mathematical Society, Series B |
Volume | 11 |
Issue number | 1 |
DOIs | |
State | Published - 2024 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024 by the author(s).