Orthogonal Rational Functions and Structured Matrices
Marc Van Barel, Dario Fasino, Luca Gemignani, Nicola Mastronardi · SIAM Journal on Matrix Analysis and Applications · 2005
The linear space of all proper rational functions with prescribed poles is considered. Given a set of points z i in the complex plane and the weights w i we define the discrete inner product $$ \langle \phi,\psi \rangle := \sum_{i=0}^n |w_i|^2 \overline{\phi(z_i)} \psi(z_i). $$