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W. Littman has shown how to obtain asymptotic approximations for Fourier transforms of surface-carried measures of the form      μ  ( X ) d A \mu (X)dA       where      d A dA       represents the area measure for the surface as a subset of Euclidean space and      μ  ( X ) \mu (X)       is a compactly supported      C ∞  {C^\infty }       function. Here we extend to the case where      μ  ( X ) \mu (X)       is an      L 2 {L^2}       function.

𝐿² asymptotes for Fourier transforms of surface- carried measures