Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems

  1. Catherine Bénéteau 1
  2. Dmitry Khavinson 1
  3. Constanze Liaw 2
  4. Daniel Seco 3
  5. Brian Simanek 4
  1. 1 University of South Florida
    info

    University of South Florida

    Tampa, Estados Unidos

    ROR https://ror.org/032db5x82

  2. 2 University of Delaware
    info

    University of Delaware

    Newark, Estados Unidos

    ROR https://ror.org/01sbq1a82

  3. 3 Universidad Carlos III de Madrid
    info

    Universidad Carlos III de Madrid

    Madrid, España

    ROR https://ror.org/03ths8210

  4. 4 Baylor University
    info

    Baylor University

    Waco, Estados Unidos

    ROR https://ror.org/005781934

Montrer des affiliations +
Revue:
Revista matemática iberoamericana

ISSN: 0213-2230

Année de publication: 2019

Volumen: 35

Número: 2

Pages: 607-642

Type: Article

DIALNET GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: Revista matemática iberoamericana

Résumé

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.

La source de données: Dialnet