@article{Aliev_Asgarova_Ismailov_2021, title={On the representation by bivariate ridge functions}, volume={73}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/263}, DOI={10.37863/umzh.v73i5.263}, abstractNote={<p>UDC 517.5</p> <p>We 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.<br><br></p>}, number={5}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Aliev, R. A. and Asgarova, A. A. and Ismailov, V. E.}, year={2021}, month={May}, pages={579 - 588} }