Measures not charging polar sets and Schrödinger equations in L p |
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作者单位: | [1]Institute of Mathematics "Simion Stoilow "of the Romanian Academy, P. O. Box 1 764, RO-014700 Bucharest, Romania and University of Pitesti, Pitesti, Romania [2]Faculty of Mathematics and Computer Science, University of Bucharest, str. Academiei 14, RO-010014 Bucharest, Romania |
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基金项目: | Supported by Deutsche Forschungsgemeinschaft (Project GZ: 436 RUM 113/23/0-1) and the Romanian Ministry of Education, Research and Youth (PN II Program, Project 373/2007, CNCSIS code ID 209) |
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摘 要: | We study the SchrSdinger equation (q -£)u +μu = f, where £ is the generator of a Borel right process and μ is a signed measure on the state space. We prove the existence and uniqueness results in Lp, 1 ≤p 〈∞ . Since we consider measures μcharging no polar set, we have to use new tools: the Revuz formula with fine versions and the appropriate Revuz correspondence, the perturbation (subordination) operators (in the sense of G Mokobodzki) induced by the regular strongly supermedian kernels. We extend the results on the SchrSdinger equation to the case of a strongly continuous sub-Markovian resolvent of contractions on Lp. If the measure μ is positive then the perturbed process solves the martingale problem for £- μ and its transition semigroup is given by the Feynman-Kac formula associated with the left continuous additive functional having μ as Revuz measure.
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关 键 词: | 薛定谔方程 极集 不充电 功能性添加剂 状态空间 马尔可夫 脂蛋白 amp |
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