中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Functional inequalities for uniformly integrable semigroups and application to essential spectrums

文献类型:期刊论文

作者Gong, FZ; Wang, FY
刊名FORUM MATHEMATICUM
出版日期2002
卷号14期号:2页码:293-313
ISSN号0933-7741
英文摘要Let (E, F, mu) be a probability space, a (not necessarily symmetric) Dirichlet form on L-2(mu), and P-t the associated sub-Markov semigroup. The equivalence of the following eight properties is studied (i) the L-2-uniform integrability of the unit ball in the Sobolev space; (ii) the super-Poincare inequality (1.2); (iii) the F-Sobolev inequality (1.3); (iv) the L2-uniform integrability of P-t; (v) the L-2-uniform integrability of the associated resolvents; (vi) the compactness of P-t; (vii) the compactness of the associated resolvents; (viii) empty essential spectrum of the associated generator. The main results can be summarized as follows. In general, (i), (ii) and (iii) are equivalent to each other, and they imply (iv) which is equivalent to (v). If P-t has transition density and, F is mu-separable, then the first seven properties from (i) to (vii) are equivalent. If in addition (E, D(E)) is symmetric, then all the above eight properties are equivalent. Moreover, the essential spectrum of the generator is estimated by using weaker functional inequalities.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000174150300006
出版者WALTER DE GRUYTER & CO
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/17902]  
专题应用数学研究所
通讯作者Gong, FZ
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
2.Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China
推荐引用方式
GB/T 7714
Gong, FZ,Wang, FY. Functional inequalities for uniformly integrable semigroups and application to essential spectrums[J]. FORUM MATHEMATICUM,2002,14(2):293-313.
APA Gong, FZ,&Wang, FY.(2002).Functional inequalities for uniformly integrable semigroups and application to essential spectrums.FORUM MATHEMATICUM,14(2),293-313.
MLA Gong, FZ,et al."Functional inequalities for uniformly integrable semigroups and application to essential spectrums".FORUM MATHEMATICUM 14.2(2002):293-313.

入库方式: OAI收割

来源:数学与系统科学研究院

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