LOCALIZATION OF ZEROS OF POLAR POLYNOMIALS ON THE UNIT DISK

Roberto S. Costas-Santos; Abdelhamid Rehouma

doi:10.1216/rmj.2024.54.995

Abstract

We derive a useful result about the zeros of the $k$ -polar polynomials on the unit circle; in particular, we obtain a circular region containing all the zeros of these polynomials. Some examples are presented.

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Roberto S. Costas-Santos. Abdelhamid Rehouma. "LOCALIZATION OF ZEROS OF POLAR POLYNOMIALS ON THE UNIT DISK." Rocky Mountain J. Math. 54 (4) 995 - 1004, August 2024. https://doi.org/10.1216/rmj.2024.54.995

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Received: 18 January 2023; Revised: 28 March 2023; Accepted: 2 April 2023; Published: August 2024

First available in Project Euclid: 25 August 2024

Digital Object Identifier: 10.1216/rmj.2024.54.995

Subjects:

Primary: 42C05

Secondary: 33C45

Keywords: Laurent series , location of zeros , orthogonal polynomials , polar polynomials , unit circle

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