Nonlinear Fourier Analysis
by Terence Tao, Christoph Thiele
Publisher: arXiv 2012
Number of pages: 98
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.
Home page url
Download or read it online for free here:
by John P. Boyd - Dover Publications
The text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, cardinal functions, etc.
by Russell Brown - University of Kentucky
These notes are intended for a course in harmonic analysis on Rn for graduate students. The background for this course is a course in real analysis which covers measure theory and the basic facts of life related to Lp spaces.
by J.P. Kahane - Tata Institute of Fundamental Research
Mean periodic functions are a generalization of periodic functions. The book considers questions such as Fourier-series, harmonic analysis, the problems of uniqueness, approximation and quasi-analyticity, as problems on mean periodic functions.
by Christopher Frye, Costas J. Efthimiou - arXiv
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to physics or mathematics undergraduates.