Comparison Problems for the Radon Transform

Explore a 53-minute lecture on comparison problems for the Radon transform, presented by Alexander Koldobsky at the Hausdorff Center for Mathematics. Delve into the question of whether two non-negative functions with Radon transforms satisfying certain inequalities have corresponding inequalities for their Lp-norms. Examine this problem for both classical and spherical Radon transforms, identifying function classes where the answer is affirmative and demonstrating negative results for functions outside these classes. Discover how these findings relate to the Busemann-Petty problem in convex geometry and learn about the generalization of Lutwak's intersection bodies. Investigate slicing inequalities connected to Oberlin-Stein type estimates for the Radon transform. Gain insights from joint work with Michael Roysdon and Artem Zvavitch in this advanced mathematical exploration.