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Nonlinear Fourier Analysis
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🧮 math.CA
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fouriernonlinearseriesclassicalnotesanaloguesanalysisanalytic
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The nonlinear Fourier transform discussed in these notes is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of the classical Fourier series, and on nonlinear analogues of classical analytic facts about Fourier series. These notes are a summary of a series of lectures given in 2003 at the Park City Mathematics Institute.
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