  In this sequel to arXiv1407.4089 by the second author, we extend to
multi-dimensional (or infinite-dimensional) settings the Goldie equation
arising in the general regular variation of `General regular variation, Popa
groups and quantifier weakening', J. Math. Anal. Appl. 483 (2020) 123610, 31
pp. (arXiv1901.05996). We extend the work there in two directions. First, we
algebraicize the theory, by systematic use of certain groups -- the Popa groups
arising in earlier work by Popa, and their relatives the Javor groups.
Secondly, we extend from the original context on the real line to
multi-dimensional (or infinite-dimensional) settings.
