4
votes
1answer
72 views

Integral with Dirac Delta

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...
0
votes
0answers
18 views

What is the modulus of smoothness for Wigner-Ville Distribution?

I heard today a seminar where the speaker talked about General Shannon Sampling operators and its modulus of smoothness. I can only find this article about the modulus of smoothness. I think you can ...
1
vote
0answers
27 views

an upper bound on Wave Front

Can you please help to understand how to solve this question: Let $f^{ij}(x)$ be a positive definite matrix smoothly varying with $x$ and define ...
3
votes
1answer
55 views

The classification of possible singular supports

I need to find the solutions of $D_{x_1}u=0$ on $\mathbb{R}^{n}$ and to classify the possible singular supports. Any one have an idea how to solve this kind of question? Thanks!
3
votes
0answers
45 views

Estimation of $\|(1-\Delta)^{\gamma/2}f\|_1$ type

Let $\phi(\xi)\in C_c^\infty(\mathbb{R}^d)$ with value $1$ in a neighborhood of the unit ball and vanishing fast outside the ball. I want to estimate $$\|(1-\Delta)^d (\cdot)^\alpha ...
3
votes
2answers
100 views

Understanding an example of a Distribution

Whilst reading the article about restrictions of distributions (generalized functions) on Wikipedia (here) I had trouble understanding the example of a distribution defined on the subset $V = (0,2) ...
1
vote
0answers
93 views

Introductory book on Distribution theory [duplicate]

Possible Duplicate: Distribution theory book Is there a good alternative to Friedlander Introduction to the Theory of Distributions ? Many thanks !
2
votes
0answers
164 views

What does it mean to carry out calculations modulo $S^{- \infty}$

I have trouble making sense of the following remark that is given in a set of lecture notes I am currently going through on my own: " Oscillatory integrals are used for the study of singularities of ...