Let M be a smooth manifold in . One may ask whether , the restriction of the Fourier transform of f to M makes sense for every f in . Since, for does not make sense pointwise, it is natural to introduce a measure σ on M and ask for an inequality
for every f in (say) the Schwartz class. Results of this kind are called restriction theorems. An excellent survey article on this subject is to be found in Tomas.
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