论文标题
Unital换向R-Elgebras的截短力矩问题
The Truncated Moment Problem for Unital Commutative R-Algebras
论文作者
论文摘要
我们调查何时在Unitual“交换元代数”的线性子空间$ b $上定义的线性功能$ l $何时接纳了整体表示W.R.T.在$ a $的字符空间的封闭子集$ k $上支持的积极ra。当$ a $配备了超级固定性时，我们为$ l $的存在提供了标准。然后，我们以此结果为基础，以证明我们的主要定理价格为$ a $，不一定配备拓扑。这使我们能够在截断的力矩问题上扩展众所周知的经典结果。
We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space of $A$. We provide a criterion for the existence of such a representation for $L$ when $A$ is equipped with a submultiplicative seminorm. We then build on this result to prove our main theorem for $A$ not necessarily equipped with a topology. This allows us to extend well-known classical results on truncated moment problems.
