Please can you guys help me to solve the following question. I couldnt even get the question.
Q. Show that an element x of an inner product space X cannot have "too many" Fourier coefficeints <x,e_k> which are "big"; here, (e_k) is given orthonormal sequence; more precisely, show that number n_m of <x,e_k> such that |<x,e_k>| > 1/m must satisfy n_m < m^2 ||x||^2.
Hint: Bessel's inequality.