Direct and inverse theorems for Szâsz-lupas type operators in simultaneous approximation
Direct results for certain family of integral type operators.
Ein Satz vom Korovkin-Typ für Ck-Räume.
Eine Verallgemeinerung eines Approximations-Satzes von C. Franchetti.
Equivalence Between K-functionals Based on Continuous Linear Transforms
2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University....
Error estimates for approximation of translation invariant operators
Estimates for the Lebesgue functions and the Nevai formula for the sinc-approximations of continuous functions on an interval.
Estimation of a smoothness parameter by spline wavelets
We consider the smoothness parameter of a function f ∈ L²(ℝ) in terms of Besov spaces , . The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0 < s*(f) < 1/2. Using p-regular (p ≥ 1) spline wavelets with exponential decay we extend them to density functions with 0 < s*(f) < p+1/2. Applying the Franklin-Strömberg wavelet p = 1, we prove that the presented estimator...
Exact bounds for some basis functions of approximation operators.
Extension of the best approximation operator in Orlicz spaces.
Extensions of linear operators from hyperplanes of
Let be a hyperplane and let be given. Denote In this paper the problem of calculating of the constant is studied. We present a complete characterization of those for which . Next we consider the case . Finally some computer examples will be presented.
Finite-Dimensional Approximation of the Inverse Frame Operator.
General uniform approximation theory by multivariate singular integral operators
We study the uniform approximation properties of general multivariate singular integral operators on , N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators to which this theory can be applied directly.
Generalizations of Durrmeyer type.
Generalized Bochner-Riesz means on spaces generated by smooth blocks
We investigate generalized Bochner-Riesz means at the critical index on spaces generated by smooth blocks and give some approximation theorems.
Global approximation by modified Baskakov type operators.
In the present paper, we prove a global direct theorem for the modified Baskakov type operators in terms of so called Ditzian-Totik modulus of smoothness.
Güteabschätzungen für den Kantorovic-Operator in der L1-Norm.
How far from can be in ?
Inequalities connected with the moduli of smootness
Kernel estimates for fractional integrals with polynomial weights