Addendum to "Invariant tori in non-degenerate nearly integrable Hamiltonian systems", RCD 6(2) 2001

For the convenience of the reader of our above mentioned paper we prove here the theorem on the approximation of periodic holomorphic functions by trigonometric polynomials in that paper without any reference to approximation theory, especially to Akhiezer's theorem. See the footnote on p. 136 in RCD 6(2) 2001.