= Bobylev identity
{c}
{title2=$\widehat Q(\xi)=\frac1{4\pi}\int\widehat f(\xi^+)\widehat f(\xi^-)\,d\sigma-\widehat f(\xi)\widehat f(0)$}
= Bobylev Fourier identity
{c}
{synonym}
For the <Maxwell molecule collision operator> and the <Fourier transform> with exponent $-i\xi\cdot v$, put $\xi^\pm=(\xi\pm|\xi|\sigma)/2$. The <angular exchange for elastic collisions>, rotation invariance of spherical surface area and factorization of the two velocity <integrals> give the displayed formula. This identity converts the collision <integral> into a spherical average of products at two related frequencies.
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