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Results tagged with pseudo-differential-operators
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user 104213
This tag is for questions regarding to the Pseudo-differential operator, acting on a space of functions on a differentiable manifold, that can locally be described by definite rules using a certain function. It satisfies estimates for the derivatives analogous to the estimates for derivatives of polynomials, which are symbols of differential operators.
2
votes
1
answer
228
views
Leibniz rule for square root of Laplacian
Let $(M,g)$ be a compact Riemannian manifold (e.g. $M=S^3$ the 3-sphere) and let $\Delta$ be the metric Laplacian on $M$. Then $\Delta$ has an $L^2(M)$ basis of eigenfunctions $\pi_m$, $$ \Delta \pi_m …
- 914
3
votes
1
answer
585
views
Characterisation of the wavefront set
I am totally new to microlocal analysis, and have been studying Jared Wunsch's notes. I have been puzzling over the properties of the wavefront set.
Let $X$ be a compact Riemannian manifold, and $\Ps …
- 914