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.