A.R. Mirotin, A.A. Atvinovskii.On multiplicative inversion for Wolff-Denjoy series ... P. 147-154

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

Received September 12, 2019

Revised November 13, 2019

Accepted November 18, 2019

Adolf Ruvimovich Mirotin, Dr. Phys.-Math. Sci., Prof., Francisk Skorina Gomel State University, g. Gomel,  246699 Belarus,
e-mail: amirotin@yandex.ru

Aleksandr Alekseevich Atvinovskii, Cand.  Sci. (Phys.-Math.), Francisk Skorina Gomel State University,  g. Gomel,  246699 Belarus,
e-mail: aatvinovskiy@gmail.com

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Cite this article as: A.R.Mirotin, A.A.Atvinovskii. On multiplicative inversion for Wolff-Denjoy series, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 147–154.