Sum of squares I: scalar functions
Functional Analysis
2022-08-18 v4
Abstract
This is the first in a series of three papers dealing with sums of squares and hypoellipticity in the infinite regime. We give a sharp sufficient condition on a smooth nonnegative function f on n-dimensional Euclidean space so that it can be written as a finite sum of squares of C^2,delta functions. Special consideration is given to analyzing the case when f vanishes only at the origin, answering a question of Bony et al.
Cite
@article{arxiv.2107.12840,
title = {Sum of squares I: scalar functions},
author = {Lyudmila Korobenko and Eric T. Sawyer},
journal= {arXiv preprint arXiv:2107.12840},
year = {2022}
}
Comments
45 pages, we thank Sullivan Francis MacDonald for pointing out an arithmetic error in the proof of Theorem 4.5, which is now weakened from its previous form. However, the main results of the paper are unaffected