Modulation property of the Fourier transform
= Modulation property of the Fourier transform
{title2=$\widehat{e^{ia\cdot x}\,d\nu}(\xi)=\widehat\nu(\xi-a)$}
= Fourier modulation and translation identity
{c}
{synonym}
Multiplication by a unit-modulus linear phase shifts the <Fourier transform>. Substituting $e^{ia\cdot x}$ into the defining integral gives the displayed identity. For a surface measure this permits independent translations of cap transforms without changing their input <norms> or angular supports.