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On some properties of finite sums of ridge functions defined on convex subsets of ℝ n

  • S. V. Konyagin
  • A. A. Kuleshov
Article

Abstract

Necessary conditions are established for the continuity of finite sums of ridge functions defined on convex subsets E of the space R n . It is shown that under some constraints imposed on the summed functions ϕ i , in the case when E is open, the continuity of the sum implies the continuity of all ϕ i . In the case when E is a convex body with nonsmooth boundary, a logarithmic estimate is obtained for the growth of the functions ϕ 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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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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