Total positivity: history, basics, and modern connections

Abstract: I will give a gentle introduction to totally positive matrices and Polya frequency functions. This includes basic examples, history, and fundamental results on total positivity, variation diminution, and sign non-reversal – as well as a few proofs to show how the main ingredients fit together. Many classical results (and one Hypothesis) from before 1955 feature in this journey. I will end by describing how Polya frequency functions connect to the Laguerre–Polya class and hence Polya–Schur multipliers, and mention 21st century incarnations of the latter.

functional analysisoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras