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math.FA2023
Sum of Squares Decompositions in Hölder Spaces
Sullivan Francis MacDonald
We investigate the number of half-regular squares required to decompose a non-negative function into a sum of squares. Each non-negative $C^{3,1}(\mathbb{R}…
math.FA2023
Regularity Preserving Sum of Squares Decompositions
Sullivan F. MacDonald
In the process of proving a sharpened form of Gårding's inequality, Fefferman & Phong demonstrated that every non-negative function can be written as a…