Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems
- Catherine Bénéteau 1
- Dmitry Khavinson 1
- Constanze Liaw 2
- Daniel Seco 3
- Brian Simanek 4
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1
University of South Florida
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2
University of Delaware
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3
Universidad Carlos III de Madrid
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4
Baylor University
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ISSN: 0213-2230
Año de publicación: 2019
Volumen: 35
Número: 2
Páginas: 607-642
Tipo: Artículo
Otras publicaciones en: Revista matemática iberoamericana
Resumen
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.