Finite and infinite dimensional Lie group structures on Riordan groups
The paper under review introduces a Frechet Lie group structure on the Riordan group and describes the corresponding Lie algebra as a vector space of infinite lower triangular matrices. Any element of this Lie algebra induces a natural linear action on the Frechet space which turns out to be related to a certain family of bivariate linear partial differential equations. One-parameter subgroups of the Riordan group are then used to solve these equations. The paper also studies the Toeplitz-Lagrange decomposition of the Riordan group into a semidirect product and stabilizer of formal power series and of Laurent series under the action induced by Riordan matrices.
bivariate linear partial differential equation
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