2 research outputs found
On polynomially integrable domains in Euclidean spaces
Let be a bounded domain in with smooth boundary. Denote
the Radon transform of
the characteristic function of the domain i.e., the
dimensional volume of the intersection with the hyperplane If the domain is an ellipsoid, then the function
is algebraic and if, in addition, the dimension is odd, then
is a polynomial with respect to Whether odd-dimensional
ellipsoids are the only bounded smooth domains with such a property? The
article is devoted to partial verification and discussion of this question