On Some Properties of Hermite–Padé Approximants to an Exponential System

Extremal properties and localization of zeros of general (including nondiagonal) type I Hermite–Padé polynomials are studied for the exponential system $\{e^{\lambda _jz}\}_{j=0}^k$ with arbitrary different complex numbers $\lambda _0,\lambda _1,\dots ,\lambda _k$. The theorems proved in the paper complement and generalize the results obtained earlier by other authors.