Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Classification and Approximation of Periodic Functions

- A. I. Stepanets
- Mathematics
- 31 July 1995

Preface. Introduction. 1. Classes of periodic functions. 2. Integral representations of deviations of linear means of Fourier series. 3. Approximations by Fourier sums in the spaces c and L1. 4.… Expand

113 6

Methods of Approximation Theory

- A. I. Stepanets
- Mathematics
- 2005

This monograph can be regarded as a result of the activity of many mathematicians of the 20th century in the field of classical Fourier series and the theory of approximation of periodic functions,… Expand

107 4

Approximation Characteristics of the Spaces Spϕ in Different Metrics

- A. I. Stepanets
- Mathematics
- 1 August 2001

AbstractWe continue the investigation of the approximation characteristics of the spaces
$$S_\phi ^p$$
introduced earlier. In particular, we establish direct and inverse theorems on the… Expand

31 4

Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp

- A. I. Stepanets, A. Serdyuk
- Mathematics
- 2002

We continue the investigation of approximation properties of the space Sp. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space… Expand

23 3

The approximation of certain classes of differentiable periodic functions of two variables by Fourier sums

- A. I. Stepanets
- Mathematics
- 1973

11 2

Approximation by fourier sums and best approximations on classes of analytic functions

- A. I. Stepanets, A. Serdyuk
- Mathematics
- 1 March 2000

We establish asymptotic equalities for upper bounds of approximations by Fourier sums and for the best approximations in the metrics of C and L1 on classes of convolutions of periodic functions that… Expand

15 2

Approximation of cauchy-type integrals in Jordan domains

- A. I. Stepanets
- Mathematics
- 1 June 1993

The concept of a generalized ψ-derivative of a function of a complex variable is introduced and applied to classify functions analytic in Jordan domains. The approximations of functions from the… Expand

3 2

Classes of functions defined on the real axis and their approximations by entire functions. II

- A. I. Stepanets
- Mathematics
- 1990

AbstractApproximation properties of functions (defined on the real axis) of the classes
$$\hat L_\beta \psi $$
introduced in the first part of the paper are studied.

25 2

Several statements for convex functions

- A. I. Stepanets
- Mathematics
- 1 May 1999

For the setM of convex-downward functions Ψ (•) vanishing at infinity, we present its decomposition into subsets with respect to the behavior of special characteristics η (Ψ;•) and μ(Ψ;•) of these… Expand

11 2

Deviation of Fourier sums on the classes of infinitely differentiable functions

- A. I. Stepanets
- Mathematics
- 1 November 1984

19 2