Smooth Extension and Interpolation of Data

Abstract: Whitney’s Extension Problem asks how we can tell if a function defined on a compact subset can be extended to a C^m function on all of R^n. Following Fefferman’s solution in 2006, much attention has been brought to the finite set analogue: Given N data points, how can we fit a smooth function through them? In this talk we will provide an introduction to this area of research, discussing some of the speaker’s recent work (joint with Fushuai Jiang and Garving K. Luli) on constrained problems where the function is required to be nonnegative or pass through certain convex sets.