On multiplicative inversion for Wolff-Denjoy series
Let a function f with real poles that form a monotone bounded sequence be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the paper states that, if we subtract the “linear part” from the function 1/f, then the remaining “fractional part” is also expanded in a Wolff-Denjoy series (its poles are also real and the coefficients of the series are negative). An application of the result to operator theory is given.