Harmonic Function Theory
by Sheldon Axler, Paul Bourdon, Wade Ramey
Publisher: Springer 2001
Number of pages: 270
This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem.
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by S.R.S. Varadhan - New York University
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...
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 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 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.