The analogue of Jacobi's theorem for simultaneous Hermitian interpolation of several functions

The sufficient conditions are found under which rational Hermite – Jacobi approximations exist for a system of functions. It is shown that under these conditions, the Hermite – Jacobi approximations coincide with the corresponding Hermite – Padе approximations. The main result in the particular case when the system consists of one function is well-known Jacobi’s theorem.