Homework Statement
Consider the space ##P_n = \text{Span}\{ e^{ik\theta};k=0,\pm 1, \dots , \pm n\}##,
with the hermitian ##L^2##-inner product
##\langle f,g\rangle = \int_{-\pi}^\pi f(\theta) \overline{g(\theta)}d\theta##.
Define operators ##A,B,C,D## as
##A = \frac{d}{d\theta}, \; \; B=...