For complex measures with Szegő coefficients of opposite signs (class T−), the paper proves a Mate-Nevai-Totik universality bound and a.e. convergence of (φ*_n φ̃_n)² along lacunary sequences, a functional version of the nonlinear Carleson problem.
Quantum signal processing and nonlinear Fourier analysis
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abstract
Elucidating a connection with nonlinear Fourier analysis, we extend a well known algorithm in quantum signal processing to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous as a function of the signal.
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One sided orthogonal polynomials and a pointwise convergence result for $SU(2)$-valued nonlinear Fourier series
For complex measures with Szegő coefficients of opposite signs (class T−), the paper proves a Mate-Nevai-Totik universality bound and a.e. convergence of (φ*_n φ̃_n)² along lacunary sequences, a functional version of the nonlinear Carleson problem.