{"title":"来自局部有界轨道的不变度量","authors":"Antoni López-Martínez","doi":"10.1007/s00025-024-02204-5","DOIUrl":null,"url":null,"abstract":"<p>Motivated by recent investigations of Sophie Grivaux and Étienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of <i>locally bounded orbit</i> for a continuous linear operator <span>\\(T:X\\longrightarrow X\\)</span> acting on a Fréchet space <i>X</i>, and we use this new notion to construct (non-trivial) <i>T</i>-invariant probability Borel measures on <span>\\((X,\\mathscr {B}(X))\\)</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"86 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Invariant measures from locally bounded orbits\",\"authors\":\"Antoni López-Martínez\",\"doi\":\"10.1007/s00025-024-02204-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Motivated by recent investigations of Sophie Grivaux and Étienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of <i>locally bounded orbit</i> for a continuous linear operator <span>\\\\(T:X\\\\longrightarrow X\\\\)</span> acting on a Fréchet space <i>X</i>, and we use this new notion to construct (non-trivial) <i>T</i>-invariant probability Borel measures on <span>\\\\((X,\\\\mathscr {B}(X))\\\\)</span>.</p>\",\"PeriodicalId\":54490,\"journal\":{\"name\":\"Results in Mathematics\",\"volume\":\"86 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00025-024-02204-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00025-024-02204-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Motivated by recent investigations of Sophie Grivaux and Étienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator \(T:X\longrightarrow X\) acting on a Fréchet space X, and we use this new notion to construct (non-trivial) T-invariant probability Borel measures on \((X,\mathscr {B}(X))\).
期刊介绍:
Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.