Разложение Обратной Величины Целой Функции С Нулями В Полосе В Ряд Крейна

Шерстюков, Владимир Борисович; Sherstyukov, V. B.

doi:10.4213/sm7771

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…Кроме того (см. статью [6] и приведенную там библиографию), различные свойства функций, допускающих представления вида ( * ), изучались и использовались в ряде работ М. Г. Крейна, Г. Л. Гамбургера, Б. Я. Левина, М. В. Келдыша и И. В. Островского, Л. де Бранжа, Ю. Ф. Коробейника, А. Боричева и М. Л. Содина, Л. С. Маергойза, В. Б. Шерстюкова по теории функций и гармоническому анализу, теории операторов и дифференциальных уравнений. Отметим также работу Н. И. Ахиезера [7].…”

Section: аналог леммы винера для рядов вольфа-данжуаunclassified

Analog for the Wiener Lemma for Wolff-Denjoy Series

Mirotin,

Atvinovskii

2019

Preprint

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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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Section: аналог леммы винера для рядов вольфа-данжуаunclassified

Analog for the Wiener Lemma for Wolff-Denjoy Series

Mirotin,

Atvinovskii

2019

Preprint

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Asymptotic Properties of Entire Functions with Given Laws of Distribution of Zeros

Sherstyukov

2021

J Math Sci

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Spectral theory of rank one perturbations of normal compact operators

Baranov

2019

St. Petersburg Math. J.

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We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis problems for such perturbations. Previously, in [10] the spectral theory of rank one perturbations was developed in the selfadjoint case. In the present paper we extend and significantly simplify most of known results in the area. We also prove an Ordering Theorem for invariant subspaces with common spectral part. This result is essentially new even for rank one perturbations of compact selfadjoint operators.

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Разложение Обратной Величины Целой Функции С Нулями В Полосе В Ряд Крейна

Cited by 3 publications

References 16 publications

Analog for the Wiener Lemma for Wolff-Denjoy Series

Analog for the Wiener Lemma for Wolff-Denjoy Series

Asymptotic Properties of Entire Functions with Given Laws of Distribution of Zeros

Spectral theory of rank one perturbations of normal compact operators

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