All Questions

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 ...

During my graduate studies I've been told that pseudo-differential operators with symbols in $S^0=S^0_{1,0}$ (the simplest class) are bounded $L^2 \to L^2$, and also $L^p \to L^p$ for all $p \in (1, \...

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 reading up on $\Psi DO$'s and trying to find some examples of symbols that are not quite so trivial. Obviously, the first example of a symbol that most people talk about is just a polynomial in $\...

Let $E\rightarrow X$ be a line bundle over a compact Riemann surface. Let $\Delta_{E}$ be the Dolbeault Laplacian $\Delta_{\overline{\partial}}$ extended to sections of $E$. Let $g_1, g_2$ be two ...

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 ...