All Questions

I am interested in the proof of the following result which gives an estimate on the Schwartz Kernel of a $\Psi$DO. There is one aspect the proof that is not clear to me which I would like to ask the ...

I'm currently working on understanding certain mean-field limits in kinetic theory, and the equations I'm working with are usually of the form $$\partial_t f +v\cdot\nabla_x f \pm c\nabla(-\Delta)^{-1}...

I have heard that the square root of the Dirichlet (or the Neumann) Laplacian is not a pseudodifferential operator on compact manifolds with boundary. The context in which this was said was that ...

In M.A. Shubin's book Pseudodifferential Operators and Spectral Theory, we have the following statement. Let $X\subset\mathbb{R}^n$ be an open set, and fix a symbol $a\in S_{\varrho,\delta}^m(X\...

Suppose we have a pseudo differential operator of principal type with a complex symbol and such that the poisson bracket of the real and imaginary parts on the characteristic set is non-negative.I ...