On the Relative Decay of Unbounded Semigroups on the Domain of the Generator

Автор(и)

  • Grigory M. Sklyar Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, Zolnierska 49, 71-210 Szczecin, Poland
  • Piotr Polak Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, Zolnierska 49, 71-210 Szczecin, Poland
  • Bartosz Wasilewski Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
    University of Szczecin, Doctoral School, Mickiewicza 16, 70-383 Szczecin, Poland

DOI:

https://doi.org/10.15407/mag20.01.094

Анотація

Дослiджується асимптотика $C_0$-пiвгрупи в областi визначення генератора. Зокрема, ми аналiзуємо поведiнку $||T(t)(A-\lambda I)^{-1}||$, коли час прямує до нескiнченностi. Нашi результати розширюють деякi наявнi результати на випадок, коли перетин спектра генератора з уявною вiссю є непорожнiм. Наведено також конструктивний приклад класу необмежених $C_0$-напiвгруп з чисто уявним точковим спектром, для яких наша теорема може бути застосована.

Mathematical Subject Classification 2020: 47D06

Ключові слова:

C0-півгрупи, асимптотична поведiнка

Посилання

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Sklyar, G. M.; Polak, P.; Wasilewski, B. On the Relative Decay of Unbounded Semigroups on the Domain of the Generator. Журн. мат. фіз. анал. геом. 2024, 20, 94–111.

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Том 20 № 1 (2024)

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