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Best n-Term Approximations by Λ-Methods in the Spaces Sϕp
We determine the exact values of the upper bounds of n-term approximations of q-ellipsoids by Λ-methods in the spaces Sϕq in the metrics of the spaces Sϕp.
On some properties of convex functions
We obtain some new results for convex-downward functions vanishing at infinity.
Approximation of Cauchy-Type Integrals
We investigate approximations of analytic functions determined by Cauchy-type integrals in Jordan domains of the complex plane. We develop, modify, and complete (in a certain sense) our earlierExpand
Approximation of Convolution Classes by Fourier Sums. New Results
We present a survey of new results related to the investigation of the rate of convergence of Fourier sums on the classes of functions defined by convolutions whose kernels have monotone FourierExpand
On some new criteria for infinite differentiability of periodic functions
AbstractWe study the set $$ \mathcal{D}^\infty $$ of infinitely differentiable periodic functions in terms of generalized $$ \bar \psi $$-derivatives defined by a pair $$ \bar \psi = (\psi _1 ,\psiExpand
On one extremal problem for positive series
The approximation properties of the spaces Sϕp introduced by Stepanets’ were studied in a series of works of Stepanets’ and his disciples. In these works, problems related to the determination ofExpand
Approximation of the $$ \bar \Psi $$-integrals of functions defined on the real axis by Fourier operators
AbstractWe find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by $$ \bar \PsiExpand