ON OPTIMAL RECOVERY OF FUNCTIONS FROM THE KOROBOV CLASS IN THE FRAMEWORK OF C(N)D – STATEMENT - Utessov А.Б. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2020)
With optimal recovery of an operator T mapping a functional class F into a normed space Y by computing units constructed from inaccurate numerical information l(N), the problems С(N)D - 1, С(N)D –2 and С(N)D –3 are successively solved. In this work, when we consider the unit operator as the operator T , the multidimensional oneperiodic Korobov class as the class F , the normalized space of functions continuous on the unit cube as the space Y , the trigonometric Fourier coefficients of the function being restored as numerical information l(N) , problems С(N)D – 2 and С(N)D –3 are solved. Namely, in the problem С(N)D – 2 the marginal error of the optimal computing unit (l^(N),\:φ _N) from the previously solved problem С(N)D - 1 was found, and in the problem С(N)D - 3 it was proved, that any computing unit with respect to trigonometric Fourier coefficients has a better marginal error, than a computing unit (l^(N),\:φ _N)