2021/07/26 by Lyudmila Korobenko, Eric T. Sawyer, Korobenko, Lyudmila +1
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #Point processes and geometric inequalities #math.FA
paper · pdf · doi:10.48550/arxiv.2107.12505
openalex publication_date 2021/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 C2,delta vector fields. We also consider slightly more general decompositions in which a single quasiconformal term need not be a sum of squares.