On the representation by sums of ridge functions

Aliev, Rashid A.; Ismailov, Vugar E.; Shahbalayeva, Tarana M.

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Institute of Mathematics and Mechanics

ISSN 2409-4986 (Print)

ISSN 2409-4994 (Online)


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Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 41 (2015), 2, 106–118

On the representation by sums of ridge functions

Rashid A. Aliev, Vugar E. Ismailov and Tarana M. Shahbalayeva

Abstract. In the current paper, we review some results on the representation by sums of ridge functions with finitely many directions. In the special case of three directions, we prove that if a function of a certain smoothness class is represented by sums of arbitrarily behaved ridge functions, then it can also be represented by sums of ridge functions of the same smoothness class.

MSC: 26B40, 39B22.

Keywords: ridge function, closed path.

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