Families of commuting formal power series and formal functional equations (Q2035012)
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scientific article; zbMATH DE number 7362515
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Families of commuting formal power series and formal functional equations |
scientific article; zbMATH DE number 7362515 |
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Families of commuting formal power series and formal functional equations (English)
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23 June 2021
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The authors discuss commuting invertible formal power series on the complex plane \(\mathbb C\). Let \(F(t,s)=\sum_{n=1} c_n(t)x^n\) denote a formal series for \(s,x \in \mathbb C\) with non-vanishing \(c_1(t)\). The commuting series form a family satisfying the formal functional equations \(F (t,F (s,x)) = F (s,F (t,x))\) (\(s,x \in \mathbb C\)) when \(c_1(t)\) takes infinitely many values. The description of this family is based on the Aczél-Jabotinsky differential equation \(H(x) \frac{\partial}{\partial x} F(t,x) = H(F(t, x))\).
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commuting formal power series
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maximal abelian subgroups
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formal functional equations
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formal partial differential equations
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