All Questions

$\newcommand{\comp}{\mathrm{comp}}$As part of my master's thesis, I am currently learning about Sobolev spaces on manifolds. From my research online, I found out, that there are a lot of ways to ...

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 ...

This question is a spin-off from Hyperbolic PDEs - Proof that the restriction of a locally $H^s$ solution to a spacelike hypersurface is locally in $H^s$ as I am trying to find a solution without ...

Suppose $X$ is a non-compact manifold. Let $P$ be an order-$0$ pseudodifferential operator on $X$ and $f:L^2(X)\rightarrow L^2(X)$ a compact operator. I'm wondering: 1) Is $P + f$ always a ...