TY - JOUR
AU - R. A. Aliev
AU - A. A. Asgarova
AU - V. E. Ismailov
PY - 2021/05/24
Y2 - 2022/08/19
TI - On the representation by bivariate ridge functions
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 73
IS - 5
SE - Research articles
DO - 10.37863/umzh.v73i5.263
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/263
AB - UDC 517.5We consider the problem of representation of a bivariate function by sums of ridge functions. It is shown that if a function of a certain smoothness class is represented by a sum of finitely many arbitrarily behaved ridge functions, then it can also be represented by a sum of ridge functions of the same smoothness class. As an example, this result is applied to a homogeneous constant coefficient partial differential equation.
ER -