Sums of squares II: matrix functions
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Publication:6373821
DOI10.1016/J.LAA.2022.12.026arXiv2107.12505MaRDI QIDQ6373821
Eric T. Sawyer, Lyudmila Korobenko
Publication date: 26 July 2021
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.
Degenerate elliptic equations (35J70) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Continuity and differentiation questions (26B05) Special properties of functions of several variables, Hölder conditions, etc. (26B35)
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