  Let a function f with real poles be expanded in a Wolff-Denjoy series with
positive coefficients. The main result of the note states that if we subtract
its linear part from the function 1/f, then the remaining fractional part of
this function will also expand into Wolff-Denjoy series (its poles are also
real, and the coefficients of the series are negative). In other words, for
Wolff-Denjoy series of the indicated form, an analogue of the well-known Wiener
lemma in the theory of Fourier series is true up to a linear term. Applications
of the result to operator theory are given.
