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 | |
【 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.
【 授权许可】
Free
【 预 览 】
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