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PreprintCC BY-NC-ND 4.0arXiv

A proof of the Baranov--Bessonov--Kapustin conjecture

Abstract

We prove the conjecture of Baranov, Bessonov and Kapustin: for a non-constant inner function θ, every bounded truncated Toeplitz operator on the model space Kθ has a bounded symbol if and only if θ is one-component

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BibTeX
@misc{bellavita2026proof,
  title = {{A proof of the Baranov--Bessonov--Kapustin conjecture}},
  author = {Carlo Bellavita and Jani A. Virtanen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26232},
  eprint = {2610.26232},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26232},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A proof of the Baranov--Bessonov--Kapustin conjecture
AU  - Carlo Bellavita
AU  - Jani A. Virtanen
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26232
UR  - https://arxiv.org/abs/2610.26232
AB  - We prove the conjecture of Baranov, Bessonov and Kapustin: for a non-constant inner function θ, every bounded truncated Toeplitz operator on the model space K_θ has a bounded symbol if and only if θ is one-component
ER  -