We consider the problem of approximation of a continuous multivariate function by sums of two ridge functions in the uniform norm. We obtain a formula for the approximation error in terms functionals generated by closed paths.
"On the error of approximation by ridge functions with two fixed directions." Tbilisi Math. J. 10 (2) 111 - 120, Feb 2017. https://doi.org/10.1515/tmj-2017-0030