2012/01/24 by Terence Tao, Christoph Thiele, Tao, Terence +1
Mathematics · #42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42
paper · pdf · doi:10.48550/arxiv.1201.5129
arxiv created 2012/01/24 · arxiv updated 2012/01/26
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.