SU(1,1) NLFT diverges pointwise for some square-summable sequences, showing that pointwise asymptotics for OPUC can fail in the Szegő class.
One sided orthogonal polynomials and a pointwise convergence result for SU(2)-valued nonlinear Fourier series.arXiv preprint, 2025.https://arxiv.org/abs/ 2507.05124
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Proves convergence of SU(1,1) and SU(2) nonlinear Fourier transforms for sparse square-summable data, yielding asymptotics for associated orthogonal polynomials on the unit circle.
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Pointwise behavior of SU(1,1) nonlinear Fourier transform
SU(1,1) NLFT diverges pointwise for some square-summable sequences, showing that pointwise asymptotics for OPUC can fail in the Szegő class.
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Convergence of sparse square-summable NLFT
Proves convergence of SU(1,1) and SU(2) nonlinear Fourier transforms for sparse square-summable data, yielding asymptotics for associated orthogonal polynomials on the unit circle.