Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices

We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences functions tridiagonal, skew-Hermitian differentiation matrix. While such L2 -orthogonal systems is well established, requires new concepts their analysis. characterize completely as appropriately weighted Fourier transforms orthogonal polynomials present number illustrative examples, inclusive Sobolev-orthogonal system whose leading N coefficients can be computed in O ( log ) $ \mathcal{O} (N\log N)$ operations.