English

An elementary proof of Takagi's theorem on the differential composition of polynomials

Classical Analysis and ODEs 2022-04-19 v1 Complex Variables

Abstract

I give a short and completely elementary proof of Takagi's 1921 theorem on the zeros of a composite polynomial f(d/dz)g(z)f(d/dz) \, g(z).

Keywords

Cite

@article{arxiv.2112.04208,
  title  = {An elementary proof of Takagi's theorem on the differential composition of polynomials},
  author = {Alan D. Sokal},
  journal= {arXiv preprint arXiv:2112.04208},
  year   = {2022}
}

Comments

LaTeX2e, 4 pages. Accepted for publication in the American Mathematical Monthly