On the Relative Decay of Unbounded Semigroups on the Domain of the Generator
We study the asymptotics of $C_0$-semigroups on the domain of the generator. In particular, we analyze the behavior of $||T(t)(A-\lambda I)^{-1}||$ as time goes to infinity. Our results extend some existing results to the case when the intersection of the spectrum of the generator with the imaginary...
Gespeichert in:
| Datum: | 2024 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
|
| Schlagworte: | |
| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1055 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Institution
Journal of Mathematical Physics, Analysis, Geometry| id |
oai:jmag.ilt.kharkiv.ua:article-1055 |
|---|---|
| record_format |
ojs |
| spelling |
oai:jmag.ilt.kharkiv.ua:article-10552024-12-10T20:10:54Z On the Relative Decay of Unbounded Semigroups on the Domain of the Generator On the Relative Decay of Unbounded Semigroups on the Domain of the Generator On the Relative Decay of Unbounded Semigroups on the Domain of the Generator Sklyar, Grigory M. Polak, Piotr Wasilewski, Bartosz C0-півгрупи асимптотична поведiнка C0-semigroups Asymptotic behavior We study the asymptotics of $C_0$-semigroups on the domain of the generator. In particular, we analyze the behavior of $||T(t)(A-\lambda I)^{-1}||$ as time goes to infinity. Our results extend some existing results to the case when the intersection of the spectrum of the generator with the imaginary axis is non-empty. We also give a constructive example of a class of unbounded $C_0$-semigroups with pure imaginary point spectrum for which our theorem is applicable. Mathematical Subject Classification 2020: 47D06 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 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024-04-01 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1055 10.15407/mag20.01.094 Journal of Mathematical Physics, Analysis, Geometry; Vol. 20 No. 1 (2024); 94–111 Журнал математической физики, анализа, геометрии; Том 20 № 1 (2024); 94–111 Журнал математичної фізики, аналізу, геометрії; Том 20 № 1 (2024); 94–111 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1055/jm20-0094e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
|
| datestamp_date |
2024-12-10T20:10:54Z |
| collection |
OJS |
| language |
English |
| topic |
C0-півгрупи асимптотична поведiнка |
| spellingShingle |
C0-півгрупи асимптотична поведiнка Sklyar, Grigory M. Polak, Piotr Wasilewski, Bartosz On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| topic_facet |
C0-півгрупи асимптотична поведiнка C0-semigroups Asymptotic behavior |
| format |
Article |
| author |
Sklyar, Grigory M. Polak, Piotr Wasilewski, Bartosz |
| author_facet |
Sklyar, Grigory M. Polak, Piotr Wasilewski, Bartosz |
| author_sort |
Sklyar, Grigory M. |
| title |
On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| title_short |
On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| title_full |
On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| title_fullStr |
On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| title_full_unstemmed |
On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| title_sort |
on the relative decay of unbounded semigroups on the domain of the generator |
| title_alt |
On the Relative Decay of Unbounded Semigroups on the Domain of the Generator On the Relative Decay of Unbounded Semigroups on the Domain of the Generator |
| description |
We study the asymptotics of $C_0$-semigroups on the domain of the generator. In particular, we analyze the behavior of $||T(t)(A-\lambda I)^{-1}||$ as time goes to infinity. Our results extend some existing results to the case when the intersection of the spectrum of the generator with the imaginary axis is non-empty. We also give a constructive example of a class of unbounded $C_0$-semigroups with pure imaginary point spectrum for which our theorem is applicable.
Mathematical Subject Classification 2020: 47D06 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2024 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1055 |
| work_keys_str_mv |
AT sklyargrigorym ontherelativedecayofunboundedsemigroupsonthedomainofthegenerator AT polakpiotr ontherelativedecayofunboundedsemigroupsonthedomainofthegenerator AT wasilewskibartosz ontherelativedecayofunboundedsemigroupsonthedomainofthegenerator |
| first_indexed |
2025-09-26T01:40:42Z |
| last_indexed |
2025-09-26T01:40:42Z |
| _version_ |
1850836863658491904 |