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### Norms and distributions

Question 1. Is there a nice or explicit way to describe the class of all distributions (generalized functions) $\mu$ on the $n$-sphere $S^n \subset \mathbb{R}^{n+1}$ for which the function
$$
F(v) := ...

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104 views

### Fourier transform and support of a distribution

Let $T \in \mathscr D'(\mathbb R^n)$ be a distribution, such that its Fourier transform $\widehat T$ is a real analytic function on $\mathbb R^n$ but it can't be continued to an entire function on ...

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85 views

### Is there an analogue of distributions in characteristic p?

Some motivation: When working over $\mathbb{C}$, distributions (in the sense of generalized functions) act as natural generators for $D$-modules (in the sense that any regular holonomic $D$-module is ...

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263 views

### Nonlinear PDE and Green functions

This is somewhat of a curiosity that can hide somewhat deeper. For a Green function of a nonlinear PDE I mean something like
$$
\partial^2\phi+V(\phi)=\delta^D(x).
$$
I do not know if a real ...

**2**

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170 views

### Spectral gap of tempered distributions

Hi,
Let $\Lambda\subset\mathbb{R}$ be an infinite discrete set of finite density (for simplicity one may take the density equals 1) and $\delta_{\lambda}$
is a unit mass located at the point ...