By Alex Iosevich,Elijah Liflyand

The Plancherel formulation says that the L^2 norm of the functionality is the same as the L^2 norm of its Fourier remodel. this means that at the least on typical, the Fourier remodel of an L^2 functionality decays at infinity. This booklet is devoted to the learn of the speed of this decay below numerous assumptions and conditions, some distance past the unique L^2 environment. Analytic and geometric houses of the underlying features engage in a continuing symbiosis which underlines the wide variety affects and purposes of the techniques below consideration.​  

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