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PreprintCC BY 4.0arXiv

Uniqueness sets in weighted ℓ2-spaces via simultaneous approximation

  • Linus Bergqvist
  • Adem Limani
  • Bartosz Malman
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Abstract

We consider a family of uniqueness problems in the setting of weighted ℓ2 Fourier spaces on the unit-circle, from the perspective of simultaneous approximation. We develop a general potential theoretical framework, which enables us to extend and unify several classical results by Ahlfors, Beurling, Frostman and Khrushchev, previously known in the more classical regimes. In addition, we prove a surprisingly sharp result that illustrates a deep discrepancy between unilateral and bilateral uniqueness sets.

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Cite

BibTeXRIS
BibTeX
@misc{bergqvist2026uniqueness,
  title = {{Uniqueness sets in weighted $\ell^2$-spaces via simultaneous approximation}},
  author = {Linus Bergqvist and Adem Limani and Bartosz Malman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24307},
  eprint = {2609.24307},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24307},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Uniqueness sets in weighted ℓ^2-spaces via simultaneous approximation
AU  - Linus Bergqvist
AU  - Adem Limani
AU  - Bartosz Malman
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24307
UR  - https://arxiv.org/abs/2609.24307
AB  - We consider a family of uniqueness problems in the setting of weighted ℓ^2 Fourier spaces on the unit-circle, from the perspective of simultaneous approximation. We develop a general potential theoretical framework, which enables us to extend and unify several classical results by Ahlfors, Beurling, Frostman and Khrushchev, previously known in the more classical regimes. In addition, we prove a surprisingly sharp result that illustrates a deep discrepancy between unilateral and bilateral uniqueness sets.
ER  -