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PreprintCC BY-NC-SA 4.0arXiv

Dry Ten Martini Problem in the Subcritical Type I Regime

  • Xianzhe Li
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Abstract

We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an application, we prove that, for every irrational frequency and every analytic potential, each subcritical Type I energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This confirms the conjecture of Ge--Jitomirskaya--You [GJY,You] in the subcritical regime.

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Cite

BibTeXRIS
BibTeX
@misc{li2026martini,
  title = {{Dry Ten Martini Problem in the Subcritical Type I Regime}},
  author = {Xianzhe Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23467},
  eprint = {2609.23467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23467},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Dry Ten Martini Problem in the Subcritical Type I Regime
AU  - Xianzhe Li
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.23467
UR  - https://arxiv.org/abs/2609.23467
AB  - We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an application, we prove that, for every irrational frequency and every analytic potential, each subcritical Type I energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This confirms the conjecture of Ge--Jitomirskaya--You [GJY,You] in the subcritical regime.
ER  -