V. V. Zhuk

About the uniform approximation on the all real axis of continuous distribution functions

The theorem of V.I. Zubov about the possibility of uniform approximation on the all real axis for an arbitrary continuous distribution function with using approaching aggregates built on the basis of the one fixed continuous distribution function is developed in a number of ways. A certain type of approaching aggregates is shown, the estimations for approximation error are given in terms of moduli of continuity.

Uniform approximation of continuous functions of bounded variation by aggregates of summatory type

Questions of uniform approximation of continuous functions of bounded variation on ℝn with the values in the Banach space are being studied by aggregates of summatory type constructed on the basis of the known function values at the nodes of a multidimensional rectangular mesh. The appraisal of accuracy is executed by means of the modulus of continuity.

Directional approximation of functions of two variables in the spaces ℒ p (R2) and ℒ p (R + 2 )

AbstractLet r ∈ N, α, t ∈ R, x ∈ R2, f: R2 → C, and denote

Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means

\Delta _{t,\alpha }^r (f,x) = \sum\limits_{k = 0}^r {( - 1)^{r - k} c_r^k f(x_1 + kt\cos \alpha ,x_2 + kt\sin \alpha ).}

Uniform Approximation of Nonperiodic Functions Defined on the Entire Axis

In this paper, we investigate the relation between the behavior of the quantity

On Uniform Approximation in R2 of Continuous Functions of Two Variables with Bounded Variation in the Sense of Hardy

\left\| {\int\limits_E {\Delta _{t,\alpha }^r (f, \cdot )\Psi _n (t)dt} } \right\|_{p,G} ,