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9
votes
2answers
1k views

Characterization of inverse differential operators

If I have a partial differential operator $p(D)$, where $p$ is a polynomial with constant coefficients and $D$ is the derivative in Euclidean space. Its inverse is easily described in Fourier space: ...
5
votes
1answer
374 views

propagation of singularities & the Schrodinger equation

I've been thinking about the following propagation of singularities result: Let $X$ be a compact manifold, and let $P$ be a differential operator (of, say, order $m$) on $X$ whose principal symbol ...