Sums of squares II: matrix functions

Abstract

This is the second in a series of three papers dealing with sums of squares and hypoellipticity in the infinitely degenerate regime. We give sharp conditions on the entries of a positive semidefinite NxN matrix function F on n-dimensional Euclidean space, whose determinant vanishes only at the origin and such that F is comparable to its diagonal matrix, in order that F is a finite sum of squares of C^2,delta vector fields. We also consider slightly more general decompositions in which a single quasiconformal term need not be a sum of squares.

31 pages, typos corrected, clarification added, the statement of Theorem 12 and the proof of Lemma 33 corrected, and a missing Lemma 34 added. Main results unchanged