A. I. Stepanets

Publications120
h-index13
Citations742
Highly Influential Citations37
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Classification and Approximation of Periodic Functions
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
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Methods of Approximation Theory
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
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Approximation Characteristics of the Spaces Spϕ in Different Metrics
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
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Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp
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
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The approximation of certain classes of differentiable periodic functions of two variables by Fourier sums
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Approximation by fourier sums and best approximations on classes of analytic functions
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
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Approximation of cauchy-type integrals in Jordan domains
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
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Classes of functions defined on the real axis and their approximations by entire functions. II
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
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
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Deviation of Fourier sums on the classes of infinitely differentiable functions
  • 19
  • 2