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Sobolev spaces and spectral theorem

Consider a generalised harmonic oscillator of the form $$ A(x,D_x) = \langle x \rangle (1-\Delta_x)\langle x \rangle, \quad x \in \mathbb{R}^n, $$ where $\langle x \rangle = (1+|x|^2)^{1/2}.$ The ...
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