Sum of squares I: scalar functions

2021/07/27 by Korobenko, Lyudmila, Sawyer, Eric T.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · doi:10.48550/arxiv.2107.12840

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 C²,delta functions. Special consideration is given to analyzing the case when f vanishes only at the origin, answering a question of Bony et al.

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