Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GENERALIZED SELF-INVERSIVE BICOMPLEX POLYNOMIALS WITH RESPECT TO THE j-CONJUGATION

  • Received : 2020.07.13
  • Accepted : 2020.12.09
  • Published : 2021.07.31
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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.

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Acknowledgement

The authors would like to express our gratitude to Professor K. Ihara and the referee for several useful comments.

References

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