Totally positive kernels, Polya frequency functions, and their transforms
Speaker:
Dominique Guillot, University of Delaware
Date and Time:
Wednesday, November 3, 2021 - 12:00pm to 12:50pm
Location:
Online
Abstract:
A kernel K:X×Y→R is said to be totally nonnegative if every finite minor of the form det(K(xi,yj))ni,j=1 is nonnegative, for any n≥1. For which functions F:R→R does the left composition operator CF(K)=F∘K preserves the total nonnegativity property? We will present several characterizations of these functions. We will also discuss many natural connections between this problem, probability theory, and group representation theory.