Geodesic
On some properties of finite sums of ridge functions defined on convex subsets of~$\mathbb R^n$
Informatics and Automation, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 193-200.

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Necessary conditions are established for the continuity of finite sums of ridge functions defined on convex subsets $E$ of the space $\mathbb R^n$. It is shown that under some constraints imposed on the summed functions $\varphi _i$, in the case when $E$ is open, the continuity of the sum implies the continuity of all $\varphi _i$. In the case when $E$ is a convex body with nonsmooth boundary, a logarithmic estimate is obtained for the growth of the functions $\varphi _i$ in the neighborhoods of the boundary points of their domains of definition. In addition, an example is constructed that demonstrates the accuracy of the estimate obtained. 
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     author = {S. V. Konyagin and A. A. Kuleshov},
     title = {On some properties of finite sums of ridge functions defined on convex subsets of~$\mathbb R^n$},
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}
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S. V. Konyagin; A. A. Kuleshov. On some properties of finite sums of ridge functions defined on convex subsets of~$\mathbb R^n$. Informatics and Automation, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 193-200. http://geodesic.mathdoc.fr/item/TRSPY_2016_293_a12/

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