Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 23 min ago
PreprintCC BY-NC-SA 4.0arXiv

Berezin--Li--Yau inequalities for Aharonov--Bohm operators

  • Michael Levitin
  • Iosif Polterovich
  • Romain Speciel
Open at sourcePDFDOICite

Abstract

We prove the sharp Berezin--Li--Yau inequality for Riesz means of order at least one for Aharonov--Bohm operators on bounded planar domains with Dirichlet boundary conditions. This confirms a conjecture posed by Frank and Hansson in 2008. We also obtain an improved lower bound for individual eigenvalues and extend it to the case of magnetic potentials with bounded magnetic field. These results are then applied to deduce estimates for Riesz means of orders between zero and one, and for Aharonov--Bohm eigenvalues on product domains.

Related

  1. Sharp harmonic-mean inequalities for Neumann and Aharonov--Bohm spectra
    Daguang Chen, Chengxi Yang
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  2. Inequalities for the Berezin Number and Norms of a Product of Three Operators
    Silvestru Sever Dragomir, Ghada N. Alnemer, Ahad Hamoud Alotaibi
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref
  3. Dispersive estimates for Dirac equations in Aharonov-Bohm magnetic fields: massive case
    Federico Cacciafesta, Piero D'Ancona, Zhiqing Yin +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Pólya's conjecture for Dirichlet eigenvalues of spherical shells and Aharonov--Bohm annuli
    Yutian Li
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Universal critical g factor for spin-1/2 Aharonov-Bohm bound states
    Vinícius Salem, Edilberto O. Silva, Fabiano M. Andrade
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{levitin2026berezinliyau,
  title = {{Berezin--Li--Yau inequalities for Aharonov--Bohm operators}},
  author = {Michael Levitin and Iosif Polterovich and Romain Speciel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40223},
  eprint = {2610.40223},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40223},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Berezin--Li--Yau inequalities for Aharonov--Bohm operators
AU  - Michael Levitin
AU  - Iosif Polterovich
AU  - Romain Speciel
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40223
UR  - https://arxiv.org/abs/2610.40223
AB  - We prove the sharp Berezin--Li--Yau inequality for Riesz means of order at least one for Aharonov--Bohm operators on bounded planar domains with Dirichlet boundary conditions. This confirms a conjecture posed by Frank and Hansson in 2008. We also obtain an improved lower bound for individual eigenvalues and extend it to the case of magnetic potentials with bounded magnetic field. These results are then applied to deduce estimates for Riesz means of orders between zero and one, and for Aharonov--Bohm eigenvalues on product domains.
ER  -