# Tagged Questions

**3**

votes

**2**answers

370 views

### Schwartz kernel theorem for topological spaces

Is there some regularizing version of Schwartz kernel theorem for topological spaces, i.e., in the form of
Every continuous linear map $A\colon C\prime(X_2) \to C(X_1)$ is given by a kernel $k \in ...

**4**

votes

**4**answers

331 views

### Reference for integral of functions taking values in a topological vector space.

(Note that I am interested in the Gelfand-Pettis integral specifically, as opposed to, for example, the Bochner integral.) I have tried Googling things like "integral topological vector space", ...

**0**

votes

**2**answers

499 views

### Is there dual space of the distributions $\mathcal{D}'(R)$?

Dear MOs,
Let $\mathcal{D}(R):=C_c^\infty(R)$ be the smooth functions with compact support. Its dual space is the space $\mathcal{D}'(R)$ of distributions. This space $\mathcal{D}(R)$ has its weak ...

**6**

votes

**5**answers

2k views

### Topology on the space of Schwartz Distributions

If we equip the Schwartz space $\mathcal{S}$ with its usual FrĂ©chet space topology, then the space of continuous linear functionals $\mathcal{S}^\ast$ is known as the space of Schwartz distributions ...

**1**

vote

**1**answer

378 views

### Equivalent references for Schwartz's book of the distribution theory

Hello,
It seems that there is no English translation of the Schwartz's book 1966. I may need to use the spaces like
$$
\dot{\mathcal{B}}(R),\quad \dot{\mathcal{B}}'(R),\quad \mathcal{B}(R),\quad ...

**3**

votes

**1**answer

558 views

### An elementary introduction of Colombeau's generalized function theory

Hello, I am wondering whether anyone know an elementary reference for Colombeau's theory on the multiplication of distributions? I encountered the problem of the square of Delta function. I need a ...

**2**

votes

**1**answer

852 views

### A good reference for the wave front set

Hello,
I am wondering whether anyone know some good references for the theory of wave front set, microlocal analysis? I have some basic knowledge of distribution theory at the level of the Rudin's ...

**11**

votes

**18**answers

6k 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.