Hermite-Padé approximation to a Nikishin type system of meromorphic functions (Q1890581)

The Nikishin system is a finite family of Cauchy transforms of finite positive Borel measures supported on the same interval. The authors consider the convergence of the rational simultaneous approximants (Hermite-Padé approximants) to the Nikishin system of two functions perturbed (additively) by rational functions. The interpolation conditions (like Padé approximation condition for one function) are quasiequally distributed between the two functions. The authors prove the convergence in capacity of the diagonal sequence of simultaneous Hermite- Padé approximants on each compact outside the common support of the measures. Under additional assumptions convergence in capacity yields uniform convergence.