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math.FA2020★ 3 cited
Multiply positive functions, critical exponent phenomena, and the Jain-Karlin-Schoenberg kernel
Apoorva Khare
We prove the converse to a result of Karlin [Trans. AMS 1964], and also strengthen his result and two results of Schoenberg [Ann. of Math. 1955]. One of the latter results concerns…
math.FA2020★ 11 cited
Totally positive kernels, Polya frequency functions, and their transforms
Alexander Belton, Dominique Guillot, Apoorva Khare +1
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…