From b3cf6a3ed2334719d5b7b047d5b5a6cbe4f14b30 Mon Sep 17 00:00:00 2001
From: Justin Gassner <justin.gassner@mailbox.org>
Date: Wed, 24 Apr 2024 04:20:39 +0200
Subject: weiter

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+%\chapter[Scales of Hilbert Spaces and Nelsons Commutator Theorem]{Scales of Hilbert Spaces\\ and Nelsons Commutator Theorem}
+\chapter{Scales of Hilbert Spaces and~Nelsons~Commutator~Theorem}
+
+\begin{theorem}{Nelson Commutator Theorem}{nelson-commutator-theorem}
+  Let $N$ be a selfadjoint operator with $N \ge I$,
+  and let $q$ be a quadratic form with the same domain.
+  Suppose that there exist constants $c_1,c_2$ such that
+  \begin{align*}
+    \abs{q(\psi',\psi)} &\le c_1 \norm{N^{1/2}\psi} \norm{N^{1/2}\psi'} & \forall \psi,\psi' \in D(N^{1/2}) \\
+    \abs{q(N\psi',\psi)-q(\psi',N\psi)} &\le c_2 \norm{N^{1/2}\psi} \norm{N^{1/2}\psi'} & \forall \psi,\psi' \in D(N^{3/2})
+  \end{align*}
+    Then the operator $q_{\mathrm{op}}$ associated to $q$ is defined on the domain of $N$
+      and is essentially selfadjoint on any core for $N$.
+\end{theorem}
+
+\cite{ReedSimon2} 
+\cite{Nelson1972} 
+
+\chapterbib
+
+%vim: syntax=mytex
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