Least square polynomials in an $L^2$ space are partial sums of the Fourier orthogonal expansions. If we were to approximate functions and their derivatives simultaneously on a domain in $R^d$ (as desired in spectral method), we would need to consider orthogonal expansions in a Sobolev space, for which the orthogonality is defined with respect to an inner product that contains derivatives. Since multiplication operators are no longer self-adjoint under such an inner product, the orthogonality is hard to understand and analyze. In the talk we will explain what is known.