**5**

votes

**3**answers

832 views

### Explicit isomorphism between distributions and universal enveloping algebra

The universal enveloping algebra of a Lie algebra $\mathfrak{g}$ is isomorphic to the algebra of distributions on the Lie group $G$ with support at the identity. The proof I have of this fact uses the ...

**3**

votes

**1**answer

1k views

### Existence of weak limits

Background: Three months ago, I asked this question, which is a bit related to the following (if the answer to it was Yes, then answer to this one would be Yes too, but since that was a No, it still ...

**5**

votes

**4**answers

1k views

### Distributions more complicated than the Dirac δ and derivatives

The responses to another question clarifies that the best known examples of distributions that are not measures, are the derivatives of the delta and such. What I want to know is: Is that the only way ...

**14**

votes

**18**answers

9k views

### Good books on theory of distributions

Hi all.
I'm looking for english books with a good coverage of distribution theory.
I'm a fan of Folland's Real analysis, but it only gives elementary notions on distributions.
Thanks in advance.

**1**

vote

**1**answer

482 views

### What do we know about the space of finite order distributions ?

Hi,
(Question updated)
My question is about the space of distributions of finite order $\mathcal{D}'_F$ (say on $\mathbb{R}^n$). What do we know about it ?
From in the information I gathered, it ...

**28**

votes

**7**answers

2k views

### What examples of distributions should I keep in mind?

I'm learning a bit about the theory of distributions. What examples of distributions will help me develop good intuition?
Definitions: Let $U$ be an open subset of $\mathbb{R}^n$. Write ...