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PreprintarXiv licencearXiv

Riesz sequences near the critical density

  • Marcin Bownik
  • Jordy Timo van Velthoven
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Abstract

We construct Riesz sequences whose Beurling density is arbitrary close to the critical density in the setting of reproducing kernel Hilbert spaces on metric measure spaces. In particular, our results apply to exponential systems on unbounded sets, nonlocalized Gabor systems and general coherent systems arising from nilpotent Lie groups. The methods used in this paper are based on our previous work on the redundancy of frames and a selector form of Weaver's conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{bownik2026riesz,
  title = {{Riesz sequences near the critical density}},
  author = {Marcin Bownik and Jordy Timo van Velthoven},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21589},
  eprint = {2609.21589},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21589},
}
RIS
TY  - UNPB
TI  - Riesz sequences near the critical density
AU  - Marcin Bownik
AU  - Jordy Timo van Velthoven
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21589
UR  - https://arxiv.org/abs/2609.21589
AB  - We construct Riesz sequences whose Beurling density is arbitrary close to the critical density in the setting of reproducing kernel Hilbert spaces on metric measure spaces. In particular, our results apply to exponential systems on unbounded sets, nonlocalized Gabor systems and general coherent systems arising from nilpotent Lie groups. The methods used in this paper are based on our previous work on the redundancy of frames and a selector form of Weaver's conjecture.
ER  -