论文标题
一个强的Feller Semigroups的单调收敛定理
A monotone convergence theorem for strong Feller semigroups
论文作者
论文摘要
对于不断增加的序列$（T_N）$的单参数半群，在波兰空间上，我们研究了极限半群，并证明了足够的条件使其具有强烈的费用。特别是，我们表明，如果后者的分解将常数1函数映射到连续函数，则强伐木特性将从近似的半群中转移到极限半群。 这对具有无限系数的$ \ mathbb {r}^d $的椭圆运算符的研究起了重要作用：我们的抽象结果使我们能够为这样的操作员分配一个半群，并表明在系数上非常轻微的规律性假设下，半群是强烈的陷入困境。 我们还提供反例，以证明我们主要结果中的假设接近最佳。
For an increasing sequence $(T_n)$ of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the strong Feller property carries over from the approximating semigroups to the limit semigroup if the resolvent of the latter maps the constant 1 function to a continuous function. This is instrumental in the study of elliptic operators on $\mathbb{R}^d$ with unbounded coefficients: our abstract result enables us to assign a semigroup to such an operator and to show that the semigroup is strongly Feller under very mild regularity assumptions on the coefficients. We also provide counterexamples to demonstrate that the assumptions in our main result are close to optimal.
