The integral-geometry tag has no usage guidance.

**3**

votes

**0**answers

83 views

### Probability that a random projection doesn't reduce the distance of a point from a subspace too much

Consider the natural uniform measure (is it called the Haar measure?) on the set of $(n-k)$-dimensional subspaces of $R^n$. We are given a $d$-dimensional affine subspace $U$ (think of $d, k \ll n$; ...

**1**

vote

**0**answers

36 views

### Combining microlocal Helgason's support and Holmgren's theorem to prove injectivity of limited-angle Radon transform

This questions is slightly related to Kashiwara's watermelon theorem and Microlocal version of Helgason's (support) and Holmgren's theorems, in which I asked for some references. Now I ...

**0**

votes

**0**answers

52 views

### Integral representation formula for convex

For $u \in \mathbb{S}^{d-1} \subset \mathbb{R}^d$, it is easy to show that:
\begin{equation}
u=c_d \int_{\mathbb{S^{d-1}}} \xi \mathbb{1}_{\left\{x \cdot u >0 \right\}}(\xi) \ ...

**0**

votes

**0**answers

75 views

### A question on Radon transform

In the book of Helgason which is called "Radon transform and integral geometry", he defines on page 2 the Radon transform on hyperplanes as:
$$ \hat{f}(\xi) = \int_{\xi} f(x) dm(x)$$
Where $dm(x)$ ...