The Plancherel formula says that the
L
sub2 norm of the function is equal to the
sub2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an
sub2 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
sub2 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.​