The Plancherel formula says that the "L" DEGREES2 norm of the
function is equal to the "L" DEGREES2 norm of its Fourier
transform. This implies that at least on average, the Fourier
transform of an "L" DEGREES2 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" DEGREES2
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.
General
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