The differential-operators tag has no wiki summary.
9
votes
1answer
229 views
Applications of Pseudodifferential Operators
I am very interested in just about anything that has to do with PDE's, and inevitably pseudodifferential operators comes up. Its obvious that such a novel way of looking at PDE's would be important, ...
8
votes
1answer
177 views
When do Harmonic polynomials constitute the kernel of a differential operator?
Let $f$ be a real polynomial of two variables. Let $\partial_f=f\left(\frac{\partial}{\partial x},\frac{\partial}{\partial y}\right)$. Let $H$ denote the space of harmonic polynomials, i.e., ...
8
votes
4answers
279 views
Determining the action of the operator $D\left(z, \frac d{dz}\right)$
This question was motivated by a question by Tobias Kienzler and its wonderful answers.
I begin as in the linked question...
Using the Taylor expansion
$$f(z+a) = \sum_{k=0}^\infty ...
0
votes
0answers
35 views
Hypoellipticity and singular support
There is a theorem that states that if $p(D)$ is a linear
partial differential operator with constant coefficients
and its fundamental solution $E$ is $C^{\infty}$ outside $\{0\}$ then
the operator ...
0
votes
1answer
85 views
On the propagation of singularities in PDE
This question might be a little generic, but i wanted to get some idea on the concept of propagation of singularities in PDE. Searching the internet i only found very complicated things about the ...
