February 5, 2019 & February 12, 2019 at 2:30 PM in Yost 306

Speaker: Kyle Taljan, MAMS PhD Candidate

Abstract

The sinc-kernel operator, which is the time and band-limiting operator, is of interest in areas such as signal processing and mathematical physics. The sinc-kernel is also of interest in random matrix theory where the related sine-kernel operator plays a prominent role. In applications, the eigenvalues of the sinc-kernel are frequently of importance. I will present results from a recent paper, Non-Asymptotic Behaviour of the Spectrum of the Sinc Kernel Operator and Related Applications, by Bonami, Jaming, and Karoui (https://arxiv.org/abs/1804.01257), which gives non-asymptotic estimates of the eigenvalues. This is of particular interest precisely because most such estimates are asymptotic in nature. I will focus on two results that demonstrate uses of the min-max and max-min characterizations of the eigenvalues of an operator (the Courant-Fischer Theorem), and, time permitting, I will talk about how this is related to my research in random matrix theory.