Fourier extension operator
= Fourier extension operator
{c}
{title2=$E_\sigma f(x)=\int e^{-ix\cdot\omega}f(\omega)\,d\sigma(\omega)$}
A <Fourier extension operator> forms an oscillatory integral from a density on a frequency surface with measure $\sigma$. The opposite sign in the phase merely reflects the output variable, so it gives identical <Lp norms>. In the usual dual formulation it is the adjoint of restricting the <Fourier transform> to that surface.