Zeros of optimal polynomial approximants and spectra of Jacobi matrices

Analysis Seminar
Wednesday, November 29, 2017 - 13:55
1 hour (actually 50 minutes)
Skiles 005
University of South Florida
    In this talk, I will discuss some polynomials that are best approximants (in some sense!) to reciprocals of functions in some analytic function spaces of the unit disk.  I will examine the extremal problem of finding a zero of minimal modulus, and will show how that extremal problem is related to the spectrum of a certain Jacobi matrix and real orthogonal polynomials on the real line.