论文标题
Dirac Delta操作员
A Dirac delta operator
论文作者
论文摘要
如果$ t $是（密集定义的）自动接合操作员，该操作员在复杂的Hilbert Space $ \ Mathcal {h} $和$ i $的身份代表身份操作员的位置，我们将在$ t $中介绍Delta函数运算符$λ\ mapstoupstoδ\ left（λi-t \ right）$。当$ t $是有界运营商时，$δ\ left（λi-t \右）$是运算符值分布。如果$ t $是无限的，则$δ\ left（λi-t \右）$是一个更通用的对象，仍然保留分布的某些属性。我们得出各种涉及$δ\ left（λi-t \右）$的操作公式，并给出了其使用的多个应用。
If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $λ\mapsto δ\left(λI-T\right) $ at $T$. When $T$ is a bounded operator, then $δ\left(λI-T\right) $ is an operator-valued distribution. If $T$ is unbounded, $δ\left(λI-T\right) $ is a more general object that still retains some properties of distributions. We derive various operative formulas involving $δ\left(λI-T\right) $ and give several applications of its usage.
