Perturbation of Dirichlet forms by measures
Perturbation of Dirichlet forms by measures
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DOI：
10.1007/bf00396775
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发表时间：
1996-04
影响因子：
1.1
通讯作者：
P. Stollmann;J. Voigt
中科院分区：
文献类型：
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作者：
P. Stollmann;J. Voigt
研究了测度μ对Dirichlet型的扰动.在适当的Kato类中定义了扰动形式−μ−+μ+，且μ+关于容量绝对连续，通过用函数逼近μ−，得到了相应半群的Lp-性质.为了处理μ+，证明了正半群的一个控制准则.若未扰动半群具有Lp-Lq-光滑性质，则扰动半群也具有Lp-Lq-光滑性质.若未扰动半群在L1上是全纯的，则对于一大类测度，扰动半群也是如此。
Perturbations of a Dirichlet formby measures μ are studied. The perturbed form−μ−+μ+is defined for μ−in a suitable Kato class and μ+absolutely continuous with respect to capacity.Lp-properties of the corresponding semigroups are derived by approximating μ−by functions. For treating μ+, a criterion for domination of positive semigroups is proved. If the unperturbed semigroup hasLp-Lq-smoothing properties the same is shown to hold for the perturbed semigroup. If the unperturbed semigroup is holomorphic onL1the same is shown to be true for the perturbed semigroup, for a large class of measures.