Zeros of Optimal Polynomial Approximants: Jacobi Matrices and Jentzsch-type Theorems
Digital Object Identifier (DOI)
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.
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Citation / Publisher Attribution
Revista Matemática Iberoamericana, v. 35, issue 2, p. 607-642
Scholar Commons Citation
Bénéteau, Catherine; Khavinson, Dmitry; Liaw, Constanze; Seco, Daniel; and Simanek, Brian, "Zeros of Optimal Polynomial Approximants: Jacobi Matrices and Jentzsch-type Theorems" (2019). Mathematics and Statistics Faculty Publications. 125.