Spectral resolution of a certain summation of series (Q1116020)

The paper deals with the spectral resolution of a linear transformation on a linear space of all sequences of real numbers, the final aim being to solve a recurrence involving the transformation. With the use of a Lie group property intrinsic to the transformation, all of its eigenvectors are obtained and the linear space is proved to be a direct sum of the one-dimensional eigenspaces. A brief comment on a method to solve certain linear recurrences is mentioned, too.