论文标题
力矩序列和差异方程
Moment sequences and difference equations
论文作者
论文摘要
我们回想起矩序序的定义和属性，并回想起其Hankel矩阵的有限等级的所有真实序列（请参阅续集中的定义）满足具有恒定系数的均匀线性方程。然后，我们分析了具有恒定系数和适当选择的初始条件的差方程并作为输入的差异方程式的案例，并且作为输入的正力矩序列具有一个正时序列的解决方案。我们给出一个一般的简单结果，并给出许多说明理论的例子。主要的简单结果指出，特征方程的奇数多样性的根必须在于产生输入中的力矩序列和适当选择的初始条件的度量的支持之外。
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant coefficients. Then we analyze cases when a difference equation with constant coefficients and suitably chosen initial conditions and having as an input a positive moment sequence has a solution that is a positive moment sequence. We give one general simple result and give many examples illustrating the theory. The main simple result states that the roots of the odd multiplicity of the characteristic equation must lie outside the support of the measure that produces the moment sequence that is in the input and the initial conditions suitably chosen.
