• Corpus ID: 231581006

Totally positive kernels, Polya frequency functions, and their transforms

@inproceedings{Belton2020TotallyPK,
  title={Totally positive kernels, Polya frequency functions, and their transforms},
  author={Alexander C. R. Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar},
  year={2020}
}
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown that such a composition operator maps the set of totally non-negative kernels to itself if and only if the function is constant or linear, or just linear if it preserves total positivity. Symmetric kernels are also discussed, with a similar outcome. These… 

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