by S.R.S. Varadhan
Publisher: New York University 2000
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.
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The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to physics or mathematics undergraduates.
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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.