Open AccessOn the representation by bivariate ridge functions
Author(s) -
R. A. Aliev,
Aysel Asgarova,
Vugar E. Ismailov
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i5.263
Subject(s) - smoothness , bivariate analysis , ridge , mathematics , function (biology) , class (philosophy) , representation (politics) , mathematical analysis , pure mathematics , constant (computer programming) , partial differential equation , homogeneous , combinatorics , statistics , computer science , geology , paleontology , evolutionary biology , artificial intelligence , politics , political science , law , biology , programming language
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.