Nonlinear Fourier Analysis
by Terence Tao, Christoph Thiele
Publisher: arXiv 2012
Number of pages: 98
Description:
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.
Download or read it online for free here:
Download link
(610KB, PDF)
Similar books
An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonicsby William Elwood Byerly - Ginn and company
From the table of contents: Development in Trigonometric Series; Convergence of Fourier's Series; Solution of Problems in Physics by the Aid of Fourier's Integrals and Fourier's Series; Zonal Harmonics; Spherical Harmonics; Cylindrical Harmonics; ...
(18768 views)
Real Harmonic Analysisby Pascal Auscher, Lashi Bandara - ANU eView
This book presents the material covered in graduate lectures delivered in 2010. Moving from the classical periodic setting to the real line, then to, nowadays, sets with minimal structures, the theory has reached a high level of applicability.
(7178 views)
Notes on Harmonic Analysisby George Benthien
Tutorial discussing some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, etc.
(12791 views)
Lectures on Topics in Mean Periodic Functions and the Two-Radius Theoremby J. Delsarte - Tata Institute of Fundamental Research
Subjects treated: transmutations of singular differential operators of the second order in the real case; new results on the theory of mean periodic functions; proof of the two-radius theorem, which is the converse of Gauss's classical theorem.
(9998 views)