期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:489
Approximation by families of generalized sampling series, realizations of generalized κ-functionals and generalized moduli of smoothness
Article
Artamonov, S.1  Runovski, Kv2  Schmeisser, H-J3 
[1] Natl Res Univ Higher Sch Econ, Moscow, Russia
[2] Lomonosov Moscow State Univ, Moscow, Russia
[3] Friedrich Schiller Univ, Jena, Germany
关键词: Moduli of smoothness;    K-functionals;    Approximation by bandlimited functions;   
DOI  :  10.1016/j.jmaa.2020.124138
来源: Elsevier
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【 摘 要 】

We study properties of realizations of generalized K-functionals and generalized moduli of smoothness in L-p(R-d) spaces with 0 < p < infinity as well as in the space C(R-d) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between the approximation error of families of generalized sampling series generated by an arbitrary generator with compact support, realizations of generalized kappa-functionals generated by homogeneous functions and generalized moduli of smoothness generated by a periodic function. Our approach covers classical approximation methods, kappa-functionals related to fractional derivatives and fractional moduli of smoothness. (C) 2020 Elsevier Inc. All rights reserved.

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