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Quantum signal processing and nonlinear Fourier analysis

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arxiv 2310.12683 v2 pith:45B6Y625 submitted 2023-10-19 quant-ph math.CA

Michel Alexis , Gevorg Mnatsakanyan , Christoph Thiele This is my paper · ORCID
classification quant-phmath.CA
keywords signalanalysisfouriernonlinearprocessingquantumalgorithmcoefficient
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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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  1. One sided orthogonal polynomials and a pointwise convergence result for $SU(2)$-valued nonlinear Fourier series

    math.CA 2025-07 conditional novelty 7.0 of 10

    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 ...

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