Complex Analysis and Dynamical Systems [book]

Mark Agranovsky, Anatoly Golberg, Fiana Jacobzon, David Shoikhet, Lawrence Zalcman
2018 Trends in Mathematics  
Let D be a bounded domain in R^n, with smooth boundary. Denote V_D(ω,t), ω∈ S^n-1, t ∈ R, the Radon transform of the characteristic function χ_D of the domain D, i.e., the (n-1)- dimensional volume of the intersection D with the hyperplane {x ∈ R^n: <ω,x>=t }. If the domain D is an ellipsoid, then the function V_D is algebraic and if, in addition, the dimension n is odd, then V(ω,t) is a polynomial with respect to t. Whether odd-dimensional ellipsoids are the only bounded smooth domains with
more » ... h a property? The article is devoted to partial verification and discussion of this question.
doi:10.1007/978-3-319-70154-7 fatcat:yi2ktyh7oza75b4o2oibf7utmm