Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation

Abstract In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-Pade approximants of a Nikishin system. The study is motivated by a mixed Hermite-Pade approximation scheme used in the construction of solutions of a Degasperis-Procesi peakon problem and germane to the analysis of the inverse spectral problem for the discrete cubic string.