论文标题
parseval框架产生的汉密尔顿人
Hamiltonians generated by Parseval frames
论文作者
论文摘要
众所周知，具有纯粹离散特征值的自动伴侣汉密尔顿人可以将相互正交投影仪与特征值作为扩展系数的（无限）线性组合。投影仪由汉密尔顿人的特征向量定义。在最近的一些论文中，这种扩展已扩展到这些特征向量形成riesz基础或最近的$ \ d $ quasi基础的情况下，\ cite {bell，bit}，而不是正常基础。在这里，我们讨论这些集合被parseval框架替换时可以做什么。这种兴趣是由物理原因激发的，尤其是由于最初定义物理系统的{\ em数学}希尔伯特空间的事实，有时还包含{\ em yralthic}系统本身无法真正占据的情况。特别是，我们显示从正统基底部到parseval帧的观测值频谱的变化。从这个角度来看，我们提出了可观察到的$ e $ connection的概念。讨论了几个例子。
It is known that self-adjoint Hamiltonians with purely discrete eigenvalues can be written as (infinite) linear combination of mutually orthogonal projectors with eigenvalues as coefficients of the expansion. The projectors are defined by the eigenvectors of the Hamiltonians. In some recent papers, this expansion has been extended to the case in which these eigenvectors form a Riesz basis or, more recently, a $\D$-quasi basis, \cite{bell,bit}, rather than an orthonormal basis. Here we discuss what can be done when these sets are replaced by Parseval frames. This interest is motivated by physical reasons, and in particular by the fact that the {\em mathematical } Hilbert space where the physical system is originally defined, contains sometimes also states which cannot really be occupied by the {\em physical} system itself. In particular, we show what changes in the spectrum of the observables, when going from orthonormal bases to Parseval frames. In this perspective we propose the notion of $E$-connection for observables. Several examples are discussed.
