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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09734 |
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| _version_ | 1866908826113933312 |
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| author | de Bruijn, Yannick Hiltunen, Erik Orvehed |
| author_facet | de Bruijn, Yannick Hiltunen, Erik Orvehed |
| contents | We show that the spectrum of the open-boundary limit of banded Toeplitz matrices is real whenever the associated symbol function is real-valued along a closed polar curve. Building on this result, we develop both analytical and numerical methods to symmetrise a class of banded non-Hermitian Toeplitz matrices whose asymptotic spectra are real. Finally, we provide a rigorous mathematical foundation for the generalised Brillouin zone, a concept widely used in non-Hermitian physics, by proving that it coincides with the polar curve on which the symbol function takes real values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09734 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mathematical Foundation for the Generalised Brillouin zone of m-banded Toeplitz operators de Bruijn, Yannick Hiltunen, Erik Orvehed Spectral Theory 15A18, 15B05, 65F15 We show that the spectrum of the open-boundary limit of banded Toeplitz matrices is real whenever the associated symbol function is real-valued along a closed polar curve. Building on this result, we develop both analytical and numerical methods to symmetrise a class of banded non-Hermitian Toeplitz matrices whose asymptotic spectra are real. Finally, we provide a rigorous mathematical foundation for the generalised Brillouin zone, a concept widely used in non-Hermitian physics, by proving that it coincides with the polar curve on which the symbol function takes real values. |
| title | Mathematical Foundation for the Generalised Brillouin zone of m-banded Toeplitz operators |
| topic | Spectral Theory 15A18, 15B05, 65F15 |
| url | https://arxiv.org/abs/2602.09734 |