Hamburger矩问题不确定时形变振子的位置算子谱测度
On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem
摘要：
在Hamburger矩不确定的情况下，计算了$q$变形振子的位置（动量）算符$X$的谱测度.本文对$q$ -振子代数生成元的具体选择进行了阐述，尽管所发展的技术适用于其它任何不确定矩问题。谱测度的Stieltjes变换$m(z)$仅用Jacobi矩阵$X$的元素表示。建立了$X$的谱测度参数值与自伴扩张之间的直接联系。
英文摘要：
The spectral measure of the position (momentum) operator $X$ for $q$-deformed oscillator is calculated in the case of the indetermine Hamburger moment problem. The exposition is given for concrete choice of generators for $q$-oscillator algebra, although developed technique apply for every other cases with indetermine moment problem. The Stieltjes transformation $m(z)$ of spectral measure is expressed in terms of the entries of Jacobi matrix $X$ only. The direct connection between values of parameters labeling the spectral measures and related selfadjoint extensions of $X$ is established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
