instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Interpolation and Approximation in Several Variables

Let X be our favorite Banach space of continuous functions on Rn  (e.g. Cm, Cm,$\alpha$, Wm,p). Given a real-valued function f defined  on an (arbitrary) given set E in Rn, we ask: How can we decide  whether f extends to a function F in X? If such an F exists, then how  small can we take its norm? What can we say about the derivatives of  F? Can we take F to depend linearly on f?

What if the set E is finite? Can we compute an F whose norm in X has  the smallest possible order of magnitude? How many computer operations  does it take? What if we ask only that F agree approximately with f on  E? What if we are allowed to discard a few points of E as "outliers";  which points should we discard?

A fundamental starting point for the above is the classical Whitney  extension theorem.

The results are joint work with Arie Israel, Bo'az Klartag, Garving  (Kevin) Luli, and Pavel Shvartsman.