Approximation Properties of the Generalized Abel-Poisson Integrals on the Weyl-Nagy Classes
Inna Kal’chuk, Yu. I. Kharkevych
Abstract
Asymptotic equalities are obtained for the least upper bounds of approximations of functions from the classes Wβ,∞r by the generalized Abel-Poisson integrals Pγ(δ),0<γ≤2, for the case r>γ in the uniform metric, which provide the solution to the Kolmogorov–Nikol’skii problem for the given method of approximation on the Weyl-Nagy classes.
Topics & Concepts
MathematicsPoisson distributionMetric (unit)Pure mathematicsPoisson's equationMathematical analysisStatisticsEconomicsOperations managementMathematical Approximation and IntegrationSpectral Theory in Mathematical PhysicsNumerical methods in inverse problems