2
votes
1answer
81 views

Support-preserving pseudodifferential operators

Let $A = F^{-1}\sigma F$ be a pseudodifferential operator acting on functions on $\mathbb R^n$, where $F$, $F^{-1}$ are the direct and inverse Fourier transforms respectively and $\sigma$ is the ...
3
votes
1answer
98 views

Interpretation of the integral “with respect to a plane wave” in terms of Radon transform

This question might have a formulation in higher dimensions, but for now let's deal with the 2 dimensional Radon transform: $\newcommand{\R}{\mathbb{R}}$ $$ Rf(\varphi,s)=\int_{-\infty}^\infty ...
2
votes
0answers
74 views

the relation between a continuous family of distributions and a distribution of 2 variables

Let X,Y be smooth manifolds and let $f:X \to C^{-\infty}(Y)$ be a continuous map, where $ C^{-\infty}(Y)$ is the space of generalized functions on $Y$ equipped with the weak topology. By Schwartz ...
1
vote
0answers
101 views

base change for distributions

For distributions on smooth manifolds one can consider the push-forward which is defined for proper maps, and the pull-back which is defined under certain condition on the wave front set see ...