Geodesic
On multiplicative inversion for Wolff-Denjoy series
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 147-154 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Wolff–Denjoy series, closed operator, left inverse operator, functional calculus. 
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A. R. Mirotin; A. A. Atvinovskii. On multiplicative inversion for Wolff-Denjoy series. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 147-154. http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a15/

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