A new closed-form expression for the solution of ODEs in a ring of distributions and its connection with the matrix algebra

02/22/2023

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by   Stefano Pozza, et al.

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A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix. This is done by studying a particular subring and connecting it with a subalgebra of infinite matrices.