This weeks analysis seminar will be given by a new member of our analysis group – Taryn Flock, who will talk On Extremizers of Certain Inequalities for the K-Plane Transform.
The talk is at 4pm in Mech-Eng G26, and as per usual there will be tea and biscuits in the common room from 3.30!
ON EXTREMIZERS OF CERTAIN INEQUALITIES FOR THE K-PLANE TRANSFORM
The Radon transform is an integral transform with applications in mathematics, tomography, and medicine. The k-plane transform is an integral transform that maps a function to its integrals over all k-dimensional planes. When k=n-1, the k-plane transform and the Radon transform coincide.
The k-plane transform is a bounded operator from Lp of Euclidean space to Lq of the Grassman manifold of all affine k-planes for certain values of q and p. Extremizers have been determined in a few cases, but most remain open. In this talk, we will focus on showing that, in the endpoint case q=n+1, extremizers are unique. Rearrangement inequalities will be a key tool.