# Tagged Questions

**5**

votes

**1**answer

193 views

### Forms satisfying the zero-energy condition on the projective plane

Theorem (Michel). A $1$-form on the projective plane is exact if and only if its integral over any projective line is equal to zero.
Is there a simple proof of this result due, I think, to R. Michel ...

**6**

votes

**1**answer

314 views

### Inversion of Radon transform by incomplete data: specific case

Let $R[f](p,t)$ denote the Radon transform of smooth function $f(x) \colon \mathbb{R}^n \to \mathbb{R}$ with compact support in $\mathbb{R}^n_+$:
$$
R[f](p,t) = \int\limits_{x \cdot p = t} f(x) dx.
...

**7**

votes

**1**answer

664 views

### Steinmetz, Laplace and Fourier Transforms

I am looking for references on Steinmetz Transform and its relation with Laplace and Fourier Transforms. There is an Italian Wikipedia page about this topic but with no references.

**3**

votes

**0**answers

127 views

### On the multidimensional Mellin transform of measures

Consider an integral transform of Borel measures supported on $\mathbb{R}^n_+$ given by
$$
f(z) =\int\limits_{\mathbb{R}^n_+} x^{z}\frac{\mu(dx)}{x}
$$
where $z = (z_1,...,z_n) \in \mathbb{C}^n$, ...

**6**

votes

**2**answers

992 views

### When is an integral transfrom trace class?

Given a measure space $(X, \mu)$ and a measurable integral kernel $k : X \times X \rightarrow \mathbb{C}$, the operator
$$ K f(\xi) =\int_{X} f(x) k(x,\xi) d \mu(x),$$
the operator $K$ is Hilbert ...