Linear Partial Differential Equations and Fourier Theory
by Marcus Pivato
Publisher: Cambridge University Press 2005
Number of pages: 619
This is a textbook for an introductory course on linear partial differential equations and initial/boundary value problems. It also provides a mathematically rigorous introduction to basic Fourier analysis, which is the main tool used to solve linear PDEs in Cartesian coordinates. Finally, it introduces basic functional analysis. This is necessary to rigorously characterize the convergence of Fourier series, and also to discuss eigenfunctions for linear differential operators.
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by Thomas Wolff - American Mathematical Society
An inside look at the techniques used and developed by the author. The book is based on a graduate course on Fourier analysis he taught at Caltech. It demonstrates how harmonic analysis can provide penetrating insights into deep aspects of analysis.
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 M. Brelot - Tata Institute of Fundamental Research
In the following we shall develop some results of the axiomatic approaches to potential theory principally some convergence theorems; they may be used as fundamental tools and applied to classical case as we shall indicate sometimes.
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.