Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 47 min ago
PreprintarXiv licencearXiv

A Balian-Low theorem for nilpotent Lie groups

  • Ulrik Enstad
  • Jordy Timo van Velthoven
Open at sourcePDFDOICite

Abstract

We prove strict necessary density conditions for smooth coherent frames and Riesz sequences in the orbit of a connected, simply connected, nilpotent Lie group. This extends previous results for homogeneous groups to general nilpotent Lie groups. The main novelty in our approach is that we prove a stability result for coherent frames and Riesz sequences based on deforming their representation rather than their index set.

Related

  1. Molnár's Theorem for split C*-by-nilpotent algebras
    Mario Galici, Gianmarco La Rosa, Manuel Mancini +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  2. A nilpotent quotient algorithm for certain infinitely presented groups and its applications
    Laurent Bartholdi, Bettina Eick, René Hartung
    International Journal of Algebra and ComputationPeer-reviewedLicence not statedFull text17 citedAlgebra & number theoryHAL
  3. A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type A
    Erez Lapid, Mark Shusterman
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. On covering systems over finite nilpotent groups and lattices
    Lian Duan, Zhenchao Ge, Biao Wang +2
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Centroids Of Partially Commutative Two-step Nilpotent Groups
    Ivan M. Buchinskiy
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{enstad2026balianlow,
  title = {{A Balian-Low theorem for nilpotent Lie groups}},
  author = {Ulrik Enstad and Jordy Timo van Velthoven},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03200},
  eprint = {2610.03200},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03200},
}
RIS
TY  - UNPB
TI  - A Balian-Low theorem for nilpotent Lie groups
AU  - Ulrik Enstad
AU  - Jordy Timo van Velthoven
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03200
UR  - https://arxiv.org/abs/2610.03200
AB  - We prove strict necessary density conditions for smooth coherent frames and Riesz sequences in the orbit of a connected, simply connected, nilpotent Lie group. This extends previous results for homogeneous groups to general nilpotent Lie groups. The main novelty in our approach is that we prove a stability result for coherent frames and Riesz sequences based on deforming their representation rather than their index set.
ER  -