Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems
Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems
We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we find the minimum possible modulus of occurring zeros via a nonlinear extremal problem associated with norms of Jacobi matrices. We examine …