Generalized self-inversive bicomplex polynomials with respect to the $j$-conjugation
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 885-895
Published online February 22, 2021
Printed July 31, 2021
Yutaka Matsui, Yuhei Sato
Kindai University; Kindai University
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
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