For a rational matrix function Φ with poles outside the unit circle, we estimate the degree of the unique superoptimal approximation 𝒜Φ by matrix functions analytic in the unit disk. We obtain sharp ...

Extending a result of Khavinson and $\acute{S}wi\cedil{a}tek$ (2003) we show that the rational harmonic function $\overline {r(z)} - z$, where r(z) is a rational function of degree n > 1, has no more ...