Id like to know methods for numerical computation of $L^2$ norm of a two dimensional trigonometric polynomial.
I have the coefficients. If I want to compute the L^1 norm, I can do so by sampling in time at a rate greater than twice of the order of the trig polynomial (Shannon sampling theorem) and then doing summation of samples which can approximate the L^1 norm integral quite well. But for L^2 norm I need to square in time domain and cannot use this procedure as squaring is non linear?
PS : I dont want to use Parseval's theorem, as it wont help if I want to compute L^3 norm of a 3 dimensional trigonometric polynomial. I want a general procedure for $L^p$ norm of a $p$ dimensional trig polynomial.