3
votes
3answers
101 views

Basic Questions about Radon Transforms

I am currently working on a problem that may be interpreted as recovering an unknown function from its Radon transform. Unfortunately I don't have any background in Radon transform, but need to ...
5
votes
1answer
196 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 ...
7
votes
1answer
330 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
1answer
689 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
0answers
129 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
2answers
1k 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 ...