Geodesic
Continuous Sums of Ridge Functions on a Convex Body and the Class VMO
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 866-873

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Sums of ridge functions on convex bodies in the space $\mathbb R^n$ are studied. It is established that, under sufficiently general constraints on the functions of one variable generating the sums, each of these sums must belong to the class VMO on each finite closed interval of its domain.
Keywords: ridge function, the class VMO. 
@article{MZM_2017_102_6_a7,
     author = {A. A. Kuleshov},
     title = {Continuous {Sums} of {Ridge} {Functions} on a {Convex} {Body} and the {Class} {VMO}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {866--873},
     publisher = {mathdoc},
     volume = {102},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a7/}
}
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A. A. Kuleshov. Continuous Sums of Ridge Functions on a Convex Body and the Class VMO. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 866-873. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a7/