On the decomposition of the Riesz operator and the expansion of the Riesz semigroup | |
Xu, GQ; Feng, DX | |
刊名 | INTEGRAL EQUATIONS AND OPERATOR THEORY
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2005-08-01 | |
卷号 | 52期号:4页码:581-594 |
关键词 | Riesz operator Riesz semigroup |
ISSN号 | 0378-620X |
DOI | 10.1007/s00020-002-1288-3 |
英文摘要 | For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues sigma(T)\{0} = {lambda(i)\ i >= 1}, denote by E(lambda(i); T) the eigen-projection corresponding to an eigenvalue lambda(i). In this paper we will show that if the operator sequence {T-n = Sigma(k=1)(n) E(lambda(k); T)T \n >= 1} is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T-p and T-r: T = T-p+T-r, where T-p is the weak limit of T-n and T-r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t >= tau. As an application, we consider the solution of transport equation on a bounded convex body. |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | BIRKHAUSER VERLAG AG |
WOS记录号 | WOS:000231771200008 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1237] ![]() |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Xu, GQ |
作者单位 | 1.Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
推荐引用方式 GB/T 7714 | Xu, GQ,Feng, DX. On the decomposition of the Riesz operator and the expansion of the Riesz semigroup[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY,2005,52(4):581-594. |
APA | Xu, GQ,&Feng, DX.(2005).On the decomposition of the Riesz operator and the expansion of the Riesz semigroup.INTEGRAL EQUATIONS AND OPERATOR THEORY,52(4),581-594. |
MLA | Xu, GQ,et al."On the decomposition of the Riesz operator and the expansion of the Riesz semigroup".INTEGRAL EQUATIONS AND OPERATOR THEORY 52.4(2005):581-594. |
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