The fundamentality of sets of ridge functions
We investigate the fundamentality of the set of all continuous ridge functions in the space C(ℝn) as well as in C(X) for a general Banach space, X. Both positive and negative results are obtained. Necessary and sufficient conditions for the fundamentality are given for certain sets of ridge functions in C(ℝn).
AMS (1991) subject classification: Primary 41A63, 41A65, 41A30, Secondary 65D15
Sun, Xingping, and Elliott Ward Cheney. "The fundamentality of sets of ridge functions." aequationes mathematicae 44, no. 2-3 (1992): 226-235.