RESTORATION OF VECTOR-VALUED FUNCTIONS BY VALUES AT THEIR LINEAR FUNCTIONALS 

Kudryavtsev Sergey Nikolaevich, candidate of physical and mathematical sciences, senior researcher, department of control of robotic devices, Federal Research Center «Computer science and control» of the Russian Academy of Sciences (Dorodnitsyn computer center of the Russian Academy of Sciences) (40 Vavilova street, Moscow, Russia), E-mail: kudrsn@yandex.ru 

519.2:8 

10.21685/2307-4205-2020-2-5 

For a class of vector-valued functions with a fixed majorant of moduli of continuity of highest derivatives, the problem of restoring functions from this class from the values on them of a given number of linear vector functionals by combining these values using scalar functions is considered. A weak asymptotic behavior is established depending on the number of functionals of the value of the best restoration accuracy in this problem. This article continues the research carried out by the author regarding classes of real-valued functions of finite smoothness, extending them to classes of vector-valued functions. The method for reconstructing vector-valued functions considered in this work is a development of the concept of a linear n-difference in relation to a situation in which approximation of vector-valued functions is carried out. The results can be used to build algorithms that restore multidimensional objects. 

vector-valued functions, finite smoothness, restoration of functions, linear functionals