Title

Zeros of Optimal Polynomial Approximants: Jacobi Matrices and Jentzsch-type Theorems

Document Type

Article

Publication Date

2019

Digital Object Identifier (DOI)

https://doi.org/10.4171/rmi/1064

Abstract

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 global properties of these zeros and prove Jentzsch-type theorems describing where they accumulate. As a consequence, we obtain detailed information regarding zeros of reproducing kernels in weighted spaces of analytic functions.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Revista Matemática Iberoamericana, v. 35, issue 2, p. 607-642

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