i can show $\sum |x|^2=\int_a^b|f(x)|^2dx$ in term of integral, or this one $|\sum x\overline y|^2=|\int_a^bf(x)\overline {g(x)}dx|^2$ but i don't know how to show this one $\sum_{i}^{n-1}\sum_{j=i+1}^{n}|(x_i\overline y_j-x_j\overline y_i)|^2$ in term of integral
$\sum_{i}^{n-1}\sum_{j=i+1}^{n}|(x_i\overline y_j-x_j\overline y_i)|^2=?$