A condition for asymptotic finite-dimensionality of an operator semigroup

Storozhuk, K. V.

doi:10.1134/s0037446611060152

Sib Math J

2011

DOI: 10.1134/s0037446611060152

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A condition for asymptotic finite-dimensionality of an operator semigroup

K. V. Storozhuk

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Cited by 3 publications

References 12 publications

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Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

Баскаков¹,

Strukov²,

Strukova³

2019

Sb. Math.

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Vector-valued functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity are investigated. The concept of the Fourier series of a function (distribution), periodic or almost periodic at infinity, with coefficients that are functions (distributions) slowly varying at infinity, is introduced. The properties of the Fourier series are investigated and an analogue of Wiener’s theorem on absolutely convergent Fourier series is obtained for functions periodic at infinity. Special attention is given to criteria ensuring that solutions of differential or difference equations are periodic or almost periodic at infinity. The central results involve theorems on the asymptotic behaviour of a bounded operator semigroup whose generator has no limit points on the imaginary axis. In addition, the concept of an asymptotically finite-dimensional operator semigroup is introduced and a theorem on the structure of such a semigroup is proved. Bibliography: 39 titles.

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Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

Баскаков¹,

Strukov²,

Strukova³

2019

Sb. Math.

View full text Add to dashboard Cite

show abstract

Solutions Almost Periodic at Infinity to Differential Equations With Unbounded Operator Coefficients

2018

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Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

Баскаков¹,

Струков²,

Strukov

et al. 2019

Математический сборник

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В статье изучаются периодические и почти периодические на бесконечности векторные функции из однородных пространств и гармоничные распределения. Определяется понятие ряда Фурье периодической и почти периодической на бесконечности функции (распределения), коэффициентами которого являются медленно меняющиеся на бесконечности функции (распределения). Изучаются свойства рядов Фурье, получен аналог теоремы Винера об абсолютно сходящихся рядах Фурье для периодических на бесконечности функций. Особое внимание уделяется критериям периодичности и почти периодичности на бесконечности решений дифференциальных и разностных уравнений. Одними из основных результатов статьи являются теоремы об асимптотическом поведении ограниченной полугруппы операторов, генератор которой не имеет предельных точек на мнимой оси. Кроме того, вводится понятие асимптотически конечномерной полугруппы операторов и доказывается теорема о структуре такой полугруппы. Библиография: 39 названий.

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A condition for asymptotic finite-dimensionality of an operator semigroup

Cited by 3 publications

References 12 publications

Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

Solutions Almost Periodic at Infinity to Differential Equations With Unbounded Operator Coefficients

Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity

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