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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