Some remarks on optimal interpolation (Q1113854)

Let \(\theta\) be a non-constant (scalar) inner function, and let T be the compression of the canonical shift on \(H^ 2\) to the subspace \(H^ 2\ominus \theta H^ 2\) (all \(H^ p\) spaces are with respect to the unit disc). For a rational function \(w\in H^{\infty}\), consider the operator w(T). An efficient procedure is described for calculation of singular values for w(T). The approach is based on the skew Toeplitz operator \(A_{\rho}\) (depending on the positive parameter \(\rho)\) defined by \(A_{\rho}=q(T)q(T)^*-\rho^{-2}p(T)p(T)^*,\) where \(w=p/q\) and p and q are polynomials.