TY - JOUR
T1 - A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems
AU - Moreira, Joel Pedro
AU - Richter, Florian Karl
N1 - Publisher Copyright:
© Cambridge University Press, 2017.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - We investigate how spectral properties of a measure-preserving system are reflected in the multiple ergodic averages arising from that system. For certain sequences , we provide natural conditions on the spectrum such that, for all , in -norm. In particular, our results apply to infinite arithmetic progressions, , Beatty sequences, , the sequence of squarefree numbers, , and the sequence of prime numbers, . We also obtain a new refinement of Szemerédi's theorem via Furstenberg's correspondence principle.
AB - We investigate how spectral properties of a measure-preserving system are reflected in the multiple ergodic averages arising from that system. For certain sequences , we provide natural conditions on the spectrum such that, for all , in -norm. In particular, our results apply to infinite arithmetic progressions, , Beatty sequences, , the sequence of squarefree numbers, , and the sequence of prime numbers, . We also obtain a new refinement of Szemerédi's theorem via Furstenberg's correspondence principle.
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U2 - 10.1017/etds.2017.61
DO - 10.1017/etds.2017.61
M3 - Article
AN - SCOPUS:85062219061
VL - 39
SP - 1042
EP - 1070
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 4
ER -