Whitney's extension problems and interpolation of data

Abstract

Given a function f : E R{double-struck} with E ⊂ R{double-struck}n, we explain how to decide whether f extends to a Cm function F on R{double-struck}n.IfE is finite, then one can efficiently compute an F as above, whose Cm norm has the least possible order of magnitude (joint work with B. Klartag). © 2008 American Mathematical Society.