I dont understand fully this lemma, and how to prove it.
For any given $n$-first Fourier coefficients of a step-wise function (sine or cosine), $\{\alpha_0,\alpha_1,\cdots,\alpha_{n}\}$ or $\{\beta_0,\beta_1,\cdots,\beta_{n}\}$, one can uniquely determine the step-wise function (numbers for $\eta_j, \ j=1,2,\cdots, n $) on a given grid of points $\xi_j, \ j=0,1,\cdots, n $.
What is the best way to start o form a poof for this?
Thanks