# 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…

## 4 Citations

Preservers of totally positive kernels and Polya frequency functions

- Mathematics
- 2021

Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided Pólya frequency functions, or totally positive kernels are treated from a unifying perspective.…

Characterizing total positivity: single vector tests via Linear Complementarity, sign non-reversal, and variation diminution

- Mathematics
- 2021

Abstract. A matrix A is called totally positive (or totally non-negative) of order k, denoted by TPk (or TNk), if all minors of size at most k are positive (or non-negative). These matrices have…

Moment-sequence transforms

- MathematicsJournal of the European Mathematical Society
- 2021

We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of…

R A ] 3 0 M ar 2 02 1 CHARACTERIZING TOTAL NEGATIVITY AND TESTING THEIR INTERVAL HULLS PROJESH

- 2021

A matrix is called totally negative (totally non-positive) of order k, if all its minors of size at most k are negative (non-positive). The objective of this article is to provide several novel…

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We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of…

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