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arXiv:1201.5129math.CA

Nonlinear Fourier Analysis

Terence Tao, Christoph Thiele

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Abstract

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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Subjects
math.CAClassical Analysis and ODEs

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  1. Generalizations of Fourier analysis (2021) 1 comment

    • > The non-linear Fourier transform (..) seems impressively obscure (I know of a total of one book reference) Are those talking about the same thing? [Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools](https://arxiv.org/abs/1202.3653)…

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