正半双线性型测度与广义本征值展开
Positive sesquilinear form measures and generalized eigenvalue expansions
摘要：
正算子测度（取值于希尔伯特空间上有界算子空间）及其推广，主要是正半双线性型测度，目的是为它们的广义本征值型展开提供一个框架.虽然有正式的相似之处，早期的方法，特殊情况下的问题，不同的文件，例如，从标准的操纵希尔伯特空间的建设，并避免了引进核型空间。该技术主要是测量理论，因此所涉及的希尔伯特空间是可分离的。结果从Naimark型膨胀结果到直接整表示和无界正规算子的相当具体的广义本征值展开式。
英文摘要：
Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized eigenvalue type expansions. Though there are formal similarities with earlier approaches to special cases of the problem, the paper differs e.g. from standard rigged Hilbert space constructions and avoids the introduction of nuclear spaces. The techniques are predominantly measure theoretic and hence the Hilbert spaces involved are separable. The results range from a Naimark type dilation result to direct integral representations and a fairly concrete generalized eigenvalue expansion for unbounded normal operators.
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。
