Bushev D. M.
Conditions of Convergence Almost Everywhere for the Convolution of a Function with Delta-Shaped Kernel to this Function
Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1461-1476
We establish sufficient conditions for the convergence of the convolution of a function with delta-shaped kernel to this function. These conditions are used for the construction of the subspaces of solutions of differential equations and systems of these equations isometric to the spaces of real functions.
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 12–19
In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation does not exceed the sum of properly chosen least upper bounds in m-and ((N ? m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality.
Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 739–753
We consider a family of special linear methods of summation of Fourier series and establish exact equalities for the approximation of classes of convolutions with even and odd kernels by polynomials generated by these methods.
Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 406-412
Asymptotically best approximation of glasses of differentiable functions by linear positive operators
Ukr. Mat. Zh. - 1985. - 37, № 2. - pp. 154 – 162