All Questions

For a one-dimensional $f(x)$, the dilation operator $f(ax)$ can be expressed as $\exp(g(D))f(x)$, where $g$ is a closed-form function. This is easily checked by e.g. formal Taylor series expansion. ...

Let $\mathcal{T}$ be a (pseudo-)differential operator that admits the following kernel representation: \begin{equation} \mathcal{T}f(x) = \int_{-\infty}^{\infty} K(x,t)f(t)dt. \end{equation} What can ...

I have a question regarding the classical trace $\text{Tr} \colon \Psi^{-\infty}(S^1)\to \mathbb C$ on pseudodifferential operators of infinite negative order (i.e. smoothing operators), defined over ...

I have a problem, which is quite urgent, as I have only today discovered an error in a proof i had in a thesis which is to be handed in tomorrow. The problem, if stated in as full generality as ...

Let $M$ be a compact manifold. If we have a pseudodifferential operator $P$ of order $0$ on $M$, then $P$ is pseudolocal, i.e., every commutator $[f,P]$ with a continuous function $f \in C(M)$ is a ...

Let's denote the set of all Pseudo-differential operators with symbol of “order” $d$ by $\Psi_d(M)$ and Sobolev space on $M$ by $H_s(M)$. It is known that If $P\in\Psi_d(M)$ Then $P$ extends to a ...