Generalized self-inversive bicomplex polynomials with respect to the $j$-conjugation

Yutaka Matsui; Yuhei Sato

doi:10.4134/BKMS.b200601

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(4): 885-895

Online first article February 22, 2021 Printed July 31, 2021

https://doi.org/10.4134/BKMS.b200601

Generalized self-inversive bicomplex polynomials with respect to the $j$-conjugation

Yutaka Matsui, Yuhei Sato

Kindai University; Kindai University

Abstract

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Abstract

In this paper, we study a kind of self-inversive polynomials in bicomplex algebra. For a bicomplex polynomial, this is the study of a relation between a kind of symmetry of its coefficients and a kind of symmetry of zeros. For our deep study, we define several new levels of self-inversivity. We prove some functional equations for standard ones, a decomposition theorem for generalized ones and a comparison theorem. Although we focus the $j$-conjugation in our study, our argument can be applied for other conjugations.

Keywords: Bicomplex analysis, self-inversive polynomial

MSC numbers: Primary 30G35, 13B25