##### Venue: Lecture Hall I, Department of Mathematics

One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in $\\R^n$. When the support is a smooth enough manifold, an almost complete picture is available. One of the early results in this direction is the following: Let $f\\in C_c^{\\infty}(d\\sigma)$, where $d\\sigma$ is the surface measure on the sphere $S^{n-1}\\subset\\R^n$. Then

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