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]
  1. [1] University of South Florida

     University of South Florida

     Estados Unidos

     
  2. [2] University of Delaware

     University of Delaware

     Estados Unidos

     
  3. [3] Universidad Carlos III de Madrid

     Universidad Carlos III de Madrid

     Madrid, España

     
  4. [4] Baylor University

     Baylor University

     Estados Unidos

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 2, 2019, págs. 607-642
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• 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.