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 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.
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 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 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.