3 problems

Interior problem conjecture. There exists a function $f\in C_c^{\infty}(\overline D)$, not identically zero in $K$, such that $\mathcal R f(L)$ vanishes for every line $L$ that int…

Power-polynomial conjecture. Then $\partial K$ is an ellipsoid; consequently, one can take $m=1$ when $n$ is odd and $m=2$ when $n$ is even.

Let $P$ and $P^{\vee}$ be the projective spaces replacing the dual projective spaces in the Radon transform, and let $D(P)_{\boldsymbol\nu}$ and $D_{\boldsymbol\nu}$ be the corresp…