Work

Locating Poles of Rational Functions in the Half Plane by Using the Backward Shift Operator

Year: 2025

Type: article

Abstract: ABSTRACT In this study, we propose a method for locating poles of rational functions within the half‐plane. This work extends the previous research on the backward shift algorithm developed for Hardy spaces in the unit disc. For rational functions, repeated application of the backward shift operator eventually yields an algebraic equation. The solutions of this equation precisely correspond to the poles of the original function, capturing both their locations and multiplicities. Based on this observation, we introduce an approach to determine these poles using discrete boundary data from the half‐plane. We analyze the approximation error and prove the convergence of the proposed method.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70246

Authors: Wen Mi, Tao Qian

Institutions: University of Electronic Science and Technology of China, Macau University of Science and Technology

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Fundo para o Desenvolvimento das Ciências e da Tecnologia, Natural Science Foundation of Sichuan Province

Awards: G2982306901, G3890633450, G7296021253