Alex Iosevich & Elijah Liflyand 
Decay of the Fourier Transform [PDF ebook] 
Analytic and Geometric Aspects

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.​

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