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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.10455 |
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Table of Contents:
- In this work we study positivity preservers $T:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}[x_1,\dots,x_n]$ with constant coefficients and define their generators $A$ if they exist, i.e., $\exp(A) = T$. We use the theory of regular Fréchet Lie groups to show the first main result. A positivity preserver with constant coefficients has a generator if and only if it is represented by an infinitely divisible measure (Main Theorem 4.7). In the second main result (Main Theorem 4.11) we use the Lévy--Khinchin formula to fully characterize the generators of positivity preservers with constant coefficients.