论文标题
较低的半框架和公制操作员
Lower semi-frames and metric operators
论文作者
论文摘要
本文讨论了将希尔伯特空间中弱可测量的功能转换为公制运算符（即严格的积极自我接合操作员）的连续框架的可能性。一个必要的条件是，与该功能相关的分析运算符的域是密集的。这项研究也是在与弱可测量功能相关的广义框架运算符的帮助下完成的，该功能比通常的框架操作员具有更好的性能。特别注意较低的半框架：确实，如果分析操作员的域是密集的，则可以将较低的半框架转换为带有（特殊的）度量算子的parseval框架。
This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated to the function be dense. The study is done also with the help of the generalized frame operator associated to a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.
