Functional inequalities for uniformly integrable semigroups and application to essential spectrums

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	Functional inequalities for uniformly integrable semigroups and application to essential spectrums
	Gong, FZ; Wang, FY
	2002
发表期刊	FORUM MATHEMATICUM
ISSN	0933-7741
卷号	14 期号:2 页码:293-313
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.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000174150300006
出版者	WALTER DE GRUYTER & CO
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17903
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.