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PreprintCC BY 4.0arXiv

On the structure of polynomial multicorrelation sequences arising from nilpotent actions

  • Jovan Andreevski
  • Felipe Hernández
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Abstract

We prove that every polynomial multicorrelation sequence arising from nilpotent actions admits a decomposition into a generalized nilsequence and a null-sequence. This resolves a long-standing question of Frantzikinakis concerning the structure of polynomial multicorrelation sequences of commuting transformations. Our proof builds upon ideas underlying the norm convergence theorem of Walsh.

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Cite

BibTeXRIS
BibTeX
@misc{andreevski2026structure,
  title = {{On the structure of polynomial multicorrelation sequences arising from nilpotent actions}},
  author = {Jovan Andreevski and Felipe Hernández},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22076},
  eprint = {2610.22076},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22076},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the structure of polynomial multicorrelation sequences arising from nilpotent actions
AU  - Jovan Andreevski
AU  - Felipe Hernández
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22076
UR  - https://arxiv.org/abs/2610.22076
AB  - We prove that every polynomial multicorrelation sequence arising from nilpotent actions admits a decomposition into a generalized nilsequence and a null-sequence. This resolves a long-standing question of Frantzikinakis concerning the structure of polynomial multicorrelation sequences of commuting transformations. Our proof builds upon ideas underlying the norm convergence theorem of Walsh.
ER  -