论文标题
关于趋于“从上方”的部门形式的序列
On sequences of sectorial forms converging `from above'
论文作者
论文摘要
我们为在复杂的希尔伯特空间中的部门形式及其相关的半群序列提供了形式的融合定理。粗略地说，近似表单$ a_n $都是通过限制表格$ a $“限制的”，但是与以前的文献相反，序列上没有单调性假设。此外，表格不应该是关闭或密集定义的。 对于扇形形式，一个人获得了相关的线性关系，其负面关系会产生一个线性运算符的强烈连续的半群。我们对形式序列的假设意味着相关线性关系的强烈分解收敛，这又意味着相应的半群的收敛性。结果通过两个示例说明了结果，其中一个与Galerkin的数值分析方法密切相关。
We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in contrast to the previous literature there is no monotonicity hypothesis on the sequence. Moreover, the forms are not supposed to be closed or densely defined. For a sectorial form one obtains an associated linear relation, whose negative generates a degenerate strongly continuous semigroup of linear operators. Our hypotheses on the sequence of forms imply strong resolvent convergence of the associated linear relations, which in turn implies convergence of the corresponding semigroups. The result is illustrated by two examples, one of them closely related to the Galerkin method of numerical analysis.
