Lectures on Topics in Mean Periodic Functions and the Two-Radius Theorem
by J. Delsarte
Publisher: Tata Institute of Fundamental Research 1961
Number of pages: 151
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 on the spherical mean for harmonic functions.
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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.
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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; ...
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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. etc...
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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.