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I Parameterization of linear operators on the holomorphisms

  1. Mar 20, 2017 #1
    Let D represent the differentiation of a single-parameter holomorphism, with respect to its parameter x. It's clear that for any sequence of holomorphisms g on x, sigma[k=0,inf](g[k](x)*D^k) is a linear operator on the space of holomorphisms. Is this a complete parameterization of the linear maps on the space of holomorphisms? If so, could someone provide a proof of this? If not, what are some counterexamples?

    P.S. I promise I'll post more interesting questions in the future :)
  2. jcsd
  3. Mar 20, 2017 #2
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