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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TIMM_2019_25_4_a15,
     author = {A. R. Mirotin and A. A. Atvinovskii},
     title = {On multiplicative inversion for {Wolff-Denjoy} series},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {147--154},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a15/}
}
TY  - JOUR
AU  - A. R. Mirotin
AU  - A. A. Atvinovskii
TI  - On multiplicative inversion for Wolff-Denjoy series
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2019
SP  - 147
EP  - 154
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a15/
LA  - ru
ID  - TIMM_2019_25_4_a15
ER  - 
%0 Journal Article
%A A. R. Mirotin
%A A. A. Atvinovskii
%T On multiplicative inversion for Wolff-Denjoy series
%J Trudy Instituta matematiki i mehaniki
%D 2019
%P 147-154
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a15/
%G ru
%F TIMM_2019_25_4_a15
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/