Gowers U2 norm
= Gowers U2 norm
{c}
{title2=$\|f\|_{U^2}$}
For a function on a finite abelian group,
$$
\|f\|_{U^2}^4=\mathbb E_{x,a,b}f(x)\overline{f(x+a)}\,\overline{f(x+b)}f(x+a+b)
=\sum_{\gamma\in\widehat G}|\widehat f(\gamma)|^4.
$$
= Gowers U2 norm
{c}
{title2=$\|f\|_{U^2}$}
For a function on a finite abelian group,
$$
\|f\|_{U^2}^4=\mathbb E_{x,a,b}f(x)\overline{f(x+a)}\,\overline{f(x+b)}f(x+a+b)
=\sum_{\gamma\in\widehat G}|\widehat f(\gamma)|^4.
$$