强连续余弦算子函数的拟fredholm和Saphar谱

Q3 Mathematics

Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI:10.2478/mjpaa-2021-0008

H. Boua

{"title":"强连续余弦算子函数的拟fredholm和Saphar谱","authors":"H. Boua","doi":"10.2478/mjpaa-2021-0008","DOIUrl":null,"url":null,"abstract":"Abstract Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"80 - 87"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function\",\"authors\":\"H. Boua\",\"doi\":\"10.2478/mjpaa-2021-0008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.\",\"PeriodicalId\":36270,\"journal\":{\"name\":\"Moroccan Journal of Pure and Applied Analysis\",\"volume\":\"7 1\",\"pages\":\"80 - 87\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moroccan Journal of Pure and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/mjpaa-2021-0008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moroccan Journal of Pure and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/mjpaa-2021-0008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 1

摘要

设(C(t))t∈𝕉是一个强连续余弦族，a是它的无穷小发生器。在本文中，我们证明了，如果C(t) - coshλt是Saphar (p。拟fredholm)算子且λt /∈iπ𝕑，则A - λ2也为Saphar (p < 0.01)。quasi-Fredholm)算子。我们通过反例证明，一般来说，反面是假的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Abstract Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Moroccan Journal of Pure and Applied Analysis Mathematics-Numerical Analysis

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

8 weeks