Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with pseudo-differential-operators
Search options not deleted
user 7333
This tag is for questions regarding to the Pseudo-differential operator, acting on a space of functions on a differentiable manifold, that can locally be described by definite rules using a certain function. It satisfies estimates for the derivatives analogous to the estimates for derivatives of polynomials, which are symbols of differential operators.
3
votes
2
answers
214
views
a question about first-order hyperbolic equations
Performing certain manipulations on pseudo-differential equations I have come across the following first order equation:
$$
D_{t}u-\lambda(t,x,D_{t},D_{x})u=0, \ \ (*)
$$
where $\lambda$ is a scalar p …
- 2,239
1
vote
second order operator with real coefficients and not locally solvable
The following example is an second order differential operator with real coefficients defined on $\mathbb{R}^{3}$ which is not solvable about origin:
$Pu=(x_{2}^{2}-x_{3}^{2})D_{1}^{2}u+(1+x_{1}^{2}) …
- 2,239
7
votes
1
answer
867
views
Pseudo-differential operators which are independent of lower order perturbations
In the area of pseudo-differential operators, we know that for elliptic type or real principal type operators reductions are independent of lower order terms. For example, if $P$ is zeroth order real …
- 2,239
4
votes
2
answers
247
views
second order operator with real coefficients and not locally solvable
This question is a follow up of the following answer I posted recently:
Counterexamples in PDE
Is there a second order partial differential operator with real coefficients which are not solvable in …
- 2,239
11
votes
2
answers
1k
views
Why take 'complex powers' of pseudo-differential operators?
Given a pseudo-differential operator $P$ of order zero, Seeley showed that the holomorphic family of operators $\lbrace P^{z} : z\in \mathbb{C} \rbrace$ of all complex powers is contained in the clas …
- 2,239
3
votes
Functions of pseudodifferential operators
Since the question posed is about the "In what way does the type of operator or the type of function matter?", I thought the following observation will be apt:
As pointed out by Liviu Nicolaescu in th …
- 2,239
7
votes
Why is symplectic geometry so important in modern PDE ?
Fourier Integral Operator is an operator which has its Schwartz kernel as a distribution whose singularities are on a Lagrangian submanifold. In fact, we can associate a FIO with an amplitude and a La …
- 2,239
4
votes
Why is symplectic geometry so important in modern PDE ?
As the cotangent space has a natural symplectic structure, we can also phrase the question as "Why is cotangent space so important in modern pde?". A nice answer for this question is given in http://m …
- 2,239
9
votes
Motivation for and history of pseudo-differential operators
A slightly different motivation for fourier integral operators and pseudo-differential operators is given in the first chapter of this book - Fourier Integral Operators, chapter V. W. Guillemin: 25 Ye …
- 2,239