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Media type:
Book
Title:
Decay of the Fourier transform
:
analytic and geometric aspects
Contains:
1. Basic properties of the Fourier transform2. Oscillatory integrals -- 3. The Fourier transform of convex and oscillating functions -- 4. The Fourier transform of a radial function -- 5. L²-average decay of the Fourier transform of a characteristic function of a convex set -- 6. L¹-average decay of the Fourier transform of a characteristic function of a convex set -- 7. Geometry of the Gauss map and lattice points in convex domains -- 8. Average decay estimates for Fourier transforms of measures supported on curves.
Description:
The Plancherel formula says that the L² norm of the function is equal to the L² norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L² 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 L² 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--
The Plancherel formula says that the L² norm of the function is equal to the L² norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L² 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 L² 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--