by S.R.S. Varadhan
Publisher: New York University 2019
Number of pages: 82
Fourier Series of a periodic function. Fejer kernel. Convergence Properties. Convolution and Fourier Series. Heat Equation. Diagonalization of convolution operators. Fourier Transforms on Rd. Multipliers and singular integral operators. Interpolation. Sobolev Spaces, Applications to PDE. Theorems of Paley-Wiener and Wiener. Hardy Spaces. Prediction. Compact Groups. Peter-Weyl Theorem.
Home page url
Download or read it online for free here:
(multiple PDF files)
by Terence Tao, Christoph Thiele - arXiv
The nonlinear Fourier transform 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.
by A. Zygmund, et al. - Princeton University Press
In the theory of convergence and summability, emphasis is placed on the phenomenon of localization whenever such occurs, and in the present paper a certain aspect of this phenomenon will be studied for the problem of best approximation as well.
by 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; ...
by 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.