Observations on power series involving logarithmic singularities

[bo198214]

Actually, not quite.

Actually what not quite?

The PDM/Carleman matrix preserves the order of arguments and the Bell matrix reverses it.

Hm perhaps then we used the term Carleman and Bell matrix in opposite meaning. If I say Bell matrix I mean the matrix that has at its \( m \)-th row the coefficients of the \( m \)-th power of the power series of \( f \). Applying this functor keeps the order of composition operands. I am not sure which reference uses the term Bell matrix or Carleman matrix so that we could verify the usual usage.

However for questions of conjugacy this difference is not really important. \( E \) is conjugate to \( T \) if and only if \( E^\sim \) is conjugate to \( T^\sim \) as \( (FTF^{-1})^\sim=(F^\sim)^{-1}T^\sim F^\sim \).