Uniformity in the Wiener-Wintner theorem for nilsequences

Abstract

We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem.

v3: 18 p., proof that the cube construction produces compact homogeneous spaces added, measurability issues in the proof of Theorem 1.5 addressed. We thank the anonymous referees for pointing out these gaps in v2

References in corpus (1)

• Ergodic averages of commuting transformations with distinct degree polynomial iterates

Cited by in corpus (9)

• Möbius disjointness for homogeneous dynamics
• Topological Wiener-Wintner ergodic theorem with polynomial weights
• (Uniform) Convergence of Twisted Ergodic Averages
• Generalized Fourier coefficients of multiplicative functions
• Nilsystems and ergodic averages along primes
• A good universal weight for nonconventional ergodic averages in norm
• Generic properties of extensions
• Cube spaces and the multiple term return times theorem
• Uniform vector-valued pointwise ergodic theorems for operators