Pointwise behavior of SU(1,1) nonlinear Fourier transform
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914597835898880 |
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| author | Denisov, Sergey A. |
| author_facet | Denisov, Sergey A. |
| contents | We show that SU(1,1) NLFT can diverge pointwise for square-summable coefficients. As a consequence, we prove that the classical pointwise asymptotics of polynomials orthogonal on the unit circle can fail for measures in the Szegö class. We also discuss some special cases when the pointwise convergence holds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_25108 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pointwise behavior of SU(1,1) nonlinear Fourier transform Denisov, Sergey A. Classical Analysis and ODEs Mathematical Physics Analysis of PDEs Dynamical Systems Spectral Theory 42C05, 42A16 We show that SU(1,1) NLFT can diverge pointwise for square-summable coefficients. As a consequence, we prove that the classical pointwise asymptotics of polynomials orthogonal on the unit circle can fail for measures in the Szegö class. We also discuss some special cases when the pointwise convergence holds. |
| title | Pointwise behavior of SU(1,1) nonlinear Fourier transform |
| topic | Classical Analysis and ODEs Mathematical Physics Analysis of PDEs Dynamical Systems Spectral Theory 42C05, 42A16 |
| url | https://arxiv.org/abs/2605.25108 |