论文标题
紧凑型情况下矩功能的内在表征
An intrinsic characterization of moment functionals in the compact case
论文作者
论文摘要
我们认为可以表示为积分W.R.T.的Unitital换向实际代数$ A $的所有线性函数$ L $的类别。在$ a $的字符空间中具有紧凑的支撑的ra尺寸。利用经典Nussbaum定理的最新概括，我们仅根据给定线性功能固有的生长条件来建立此类力矩功能的新表征。据我们所知，我们的结果是第一个准确确定代表ra量度的紧凑支持。我们还用最大的阿基米德二次模块来描述紧凑的支持，该模块上$ l $是非负数的，并且在最小的士兵seminorm w.r.t.方面。哪个$ L $是连续的。此外，我们得出了一个用于计算紧凑型支持中每个单身子的度量的公式，这反过来又提供了必要且充分的条件，使支持成为有限的集合。最后，还研究了与我们的拓扑代数生长条件有关的一些方面。
We consider the class of all linear functionals $L$ on a unital commutative real algebra $A$ that can be represented as an integral w.r.t. to a Radon measure with compact support in the character space of $A$. Exploiting a recent generalization of the classical Nussbaum theorem, we establish a new characterization of this class of moment functionals solely in terms of a growth condition intrinsic to the given linear functional. To the best of our knowledge, our result is the first to exactly identify the compact support of the representing Radon measure. We also describe the compact support in terms of the largest Archimedean quadratic module on which $L$ is non-negative and in terms of the smallest submultiplicative seminorm w.r.t. which $L$ is continuous. Moreover, we derive a formula for computing the measure of each singleton in the compact support, which in turn gives a necessary and sufficient condition for the support to be a finite set. Finally, some aspects related to our growth condition for topological algebras are also investigated.
