Establishes global uniform Cesàro asymptotics for reflected orthogonal polynomials on the unit circle for Szegő-class measures, extending the local Máté-Nevai-Totik result.
Pointwise behavior of SU(1,1) nonlinear Fourier transform
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abstract
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 Szeg\"o class. We also discuss some special cases when the pointwise convergence holds.
fields
math.CA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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.
citing papers explorer
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From local to global asymptotic behaviour of orthogonal polynomials
Establishes global uniform Cesàro asymptotics for reflected orthogonal polynomials on the unit circle for Szegő-class measures, extending the local Máté-Nevai-Totik result.
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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.