On the representation by sums of ridge functions

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

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku

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

Received: 15.06.2015
Accepted: 25.11.2015

Language: English