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arXiv · 1908.08029

Analog for the Wiener Lemma for Wolff-Denjoy Series

A. R. Mirotin·A. A. Atvinovskii
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Abstract

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.

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A. R. Mirotin, A. A. Atvinovskii. 2019-08-21. Analog for the Wiener Lemma for Wolff-Denjoy Series. https://arxiv.org/abs/1908.08029

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