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The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

Decay of the Fourier Transform: Analytic and Geometric Aspects

Foreword.- Introduction.- Chapter 1. Basic properties of the Fourier transform.- Chapter 2. Oscillatory integrals and Fourier transforms in one variable.- Chapter 3. The Fourier transform of an oscillating function.- Chapter 4. The Fourier transform of a radial function.- Chapter 5. Multivariate extensions.- Appendix.- Bibliography.